My modem module can dial out and make a data connection and it always answers voice calls, but it won't anwser data calls.

1. Check that S-register 0 is not set to zero.

2. Set the Incoming Call bearer parameter to data using this command:

AT+CICB=0


Incoming Call bearer +CICB
Description:
This specific command is used to set the type of incoming calls when no incoming bearer is given.
Values:
0 - Data
1 - Fax
2 - Speech
3 - Data once (10 minute timeout)
4 - Fax once (10 minute timeout)