Hello Mihaelapetrescu,
Welcome to the community!
Firstly, which version of the Lumia 640 LTE phone do you have? Where did you purchase the phone? These are the band/frequency specifications for that phone from the Microsoft website:
| Cellular connectivity2 |
GSM network: 850 MHz, 900 MHz, 1800 MHz, 1900 MHz
WCDMA network: Band 5 (850 MHz), Band 8 (900 MHz), Band 1 (2100 MHz)
LTE FDD network: Band 8 (900MHz), Band 20 (800MHz), Band 1 (2100 MHz), Band 3 (1800 MHz), Band 7 (2600 MHz)
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Judging by those specifications, that version of the phone has both of the compatible bands/frequencies for 2G and only one compatible band/frequency for '3G'. Note that Rogers intends to decommission the GSM network by December 31, 2020 (see here). With regards to LTE, that phone only has one compatible band/frequency. You can verify the compatible bands/frequencies here. While the phone should work for data, coverage depends on corresponding bands/frequencies on your surrounding cellular towers. You can get an idea of your local cellular towers here.
There do appear to be multiple versions of the phone (see here) which may have additional compatible bands/frequencies.
Have you verified the phone is using the correct APN? Since the phone is LTE-capable, it should be using ltemobile.apn. You can verify those settings here.
Have you tried to enable roaming data? Occasionally, some phones from abroad might think they are roaming if outside of their intended target market even though they are using a local SIM.
Have you been able to use data with a different phone? Is it possible that there might be a data block on your account?
Hope this helps 
Cheers
Hey @mihaelapetrescu!
Let the Community know if you were able to get this sorted out!
We'd love to know what worked for you.
