Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2005))\).
|
Total |
New |
Old |
Modular forms
| 162400 |
148595 |
13805 |
Cusp forms
| 159201 |
146199 |
13002 |
Eisenstein series
| 3199 |
2396 |
803 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2005))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
2005.2.a |
\(\chi_{2005}(1, \cdot)\) |
2005.2.a.a |
1 |
1 |
2005.2.a.b |
1 |
2005.2.a.c |
3 |
2005.2.a.d |
25 |
2005.2.a.e |
29 |
2005.2.a.f |
37 |
2005.2.a.g |
37 |
2005.2.b |
\(\chi_{2005}(1204, \cdot)\) |
n/a |
200 |
1 |
2005.2.c |
\(\chi_{2005}(2004, \cdot)\) |
n/a |
200 |
1 |
2005.2.d |
\(\chi_{2005}(801, \cdot)\) |
n/a |
134 |
1 |
2005.2.e |
\(\chi_{2005}(381, \cdot)\) |
n/a |
268 |
2 |
2005.2.j |
\(\chi_{2005}(1584, \cdot)\) |
n/a |
400 |
2 |
2005.2.k |
\(\chi_{2005}(841, \cdot)\) |
n/a |
536 |
4 |
2005.2.m |
\(\chi_{2005}(356, \cdot)\) |
n/a |
536 |
4 |
2005.2.n |
\(\chi_{2005}(499, \cdot)\) |
n/a |
792 |
4 |
2005.2.p |
\(\chi_{2005}(831, \cdot)\) |
n/a |
536 |
4 |
2005.2.q |
\(\chi_{2005}(29, \cdot)\) |
n/a |
800 |
4 |
2005.2.r |
\(\chi_{2005}(39, \cdot)\) |
n/a |
800 |
4 |
2005.2.u |
\(\chi_{2005}(147, \cdot)\) |
n/a |
1592 |
8 |
2005.2.v |
\(\chi_{2005}(133, \cdot)\) |
n/a |
1592 |
8 |
2005.2.w |
\(\chi_{2005}(164, \cdot)\) |
n/a |
1600 |
8 |
2005.2.bb |
\(\chi_{2005}(56, \cdot)\) |
n/a |
1072 |
8 |
2005.2.bc |
\(\chi_{2005}(51, \cdot)\) |
n/a |
2680 |
20 |
2005.2.be |
\(\chi_{2005}(114, \cdot)\) |
n/a |
3168 |
16 |
2005.2.bf |
\(\chi_{2005}(126, \cdot)\) |
n/a |
2144 |
16 |
2005.2.bh |
\(\chi_{2005}(16, \cdot)\) |
n/a |
2680 |
20 |
2005.2.bi |
\(\chi_{2005}(224, \cdot)\) |
n/a |
4000 |
20 |
2005.2.bj |
\(\chi_{2005}(14, \cdot)\) |
n/a |
4000 |
20 |
2005.2.bk |
\(\chi_{2005}(48, \cdot)\) |
n/a |
6368 |
32 |
2005.2.bl |
\(\chi_{2005}(33, \cdot)\) |
n/a |
6368 |
32 |
2005.2.bo |
\(\chi_{2005}(81, \cdot)\) |
n/a |
5360 |
40 |
2005.2.bt |
\(\chi_{2005}(4, \cdot)\) |
n/a |
8000 |
40 |
2005.2.bu |
\(\chi_{2005}(9, \cdot)\) |
n/a |
15840 |
80 |
2005.2.bx |
\(\chi_{2005}(11, \cdot)\) |
n/a |
10720 |
80 |
2005.2.by |
\(\chi_{2005}(12, \cdot)\) |
n/a |
31840 |
160 |
2005.2.cb |
\(\chi_{2005}(3, \cdot)\) |
n/a |
31840 |
160 |
"n/a" means that newforms for that character have not been added to the database yet