Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3332))\).
|
Total |
New |
Old |
Modular forms
| 5168 |
1743 |
3425 |
Cusp forms
| 368 |
289 |
79 |
Eisenstein series
| 4800 |
1454 |
3346 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3332))\)
We only show spaces with odd 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 |
3332.1.c |
\(\chi_{3332}(2449, \cdot)\) |
None |
0 |
1 |
3332.1.d |
\(\chi_{3332}(1667, \cdot)\) |
None |
0 |
1 |
3332.1.g |
\(\chi_{3332}(883, \cdot)\) |
3332.1.g.a |
1 |
1 |
3332.1.g.b |
1 |
3332.1.g.c |
1 |
3332.1.g.d |
1 |
3332.1.g.e |
1 |
3332.1.g.f |
2 |
3332.1.g.g |
2 |
3332.1.g.h |
2 |
3332.1.g.i |
8 |
3332.1.h |
\(\chi_{3332}(1665, \cdot)\) |
None |
0 |
1 |
3332.1.j |
\(\chi_{3332}(293, \cdot)\) |
None |
0 |
2 |
3332.1.m |
\(\chi_{3332}(2843, \cdot)\) |
3332.1.m.a |
2 |
2 |
3332.1.m.b |
2 |
3332.1.m.c |
2 |
3332.1.n |
\(\chi_{3332}(509, \cdot)\) |
None |
0 |
2 |
3332.1.o |
\(\chi_{3332}(67, \cdot)\) |
3332.1.o.a |
2 |
2 |
3332.1.o.b |
2 |
3332.1.o.c |
2 |
3332.1.o.d |
2 |
3332.1.o.e |
4 |
3332.1.o.f |
4 |
3332.1.o.g |
16 |
3332.1.r |
\(\chi_{3332}(851, \cdot)\) |
None |
0 |
2 |
3332.1.s |
\(\chi_{3332}(1293, \cdot)\) |
None |
0 |
2 |
3332.1.w |
\(\chi_{3332}(491, \cdot)\) |
3332.1.w.a |
4 |
4 |
3332.1.w.b |
4 |
3332.1.w.c |
4 |
3332.1.w.d |
4 |
3332.1.y |
\(\chi_{3332}(1273, \cdot)\) |
None |
0 |
4 |
3332.1.z |
\(\chi_{3332}(1109, \cdot)\) |
None |
0 |
4 |
3332.1.bc |
\(\chi_{3332}(667, \cdot)\) |
3332.1.bc.a |
4 |
4 |
3332.1.bc.b |
4 |
3332.1.bc.c |
4 |
3332.1.bc.d |
4 |
3332.1.bd |
\(\chi_{3332}(237, \cdot)\) |
None |
0 |
6 |
3332.1.be |
\(\chi_{3332}(407, \cdot)\) |
3332.1.be.a |
6 |
6 |
3332.1.be.b |
6 |
3332.1.be.c |
12 |
3332.1.bh |
\(\chi_{3332}(239, \cdot)\) |
None |
0 |
6 |
3332.1.bi |
\(\chi_{3332}(69, \cdot)\) |
None |
0 |
6 |
3332.1.bk |
\(\chi_{3332}(197, \cdot)\) |
None |
0 |
8 |
3332.1.bn |
\(\chi_{3332}(979, \cdot)\) |
3332.1.bn.a |
8 |
8 |
3332.1.bn.b |
8 |
3332.1.bn.c |
8 |
3332.1.bn.d |
8 |
3332.1.bp |
\(\chi_{3332}(263, \cdot)\) |
3332.1.bp.a |
8 |
8 |
3332.1.bp.b |
8 |
3332.1.bp.c |
8 |
3332.1.bp.d |
8 |
3332.1.br |
\(\chi_{3332}(117, \cdot)\) |
None |
0 |
8 |
3332.1.bt |
\(\chi_{3332}(183, \cdot)\) |
None |
0 |
12 |
3332.1.bw |
\(\chi_{3332}(13, \cdot)\) |
None |
0 |
12 |
3332.1.by |
\(\chi_{3332}(341, \cdot)\) |
None |
0 |
12 |
3332.1.bz |
\(\chi_{3332}(375, \cdot)\) |
None |
0 |
12 |
3332.1.cc |
\(\chi_{3332}(135, \cdot)\) |
3332.1.cc.a |
12 |
12 |
3332.1.cc.b |
12 |
3332.1.cc.c |
24 |
3332.1.cd |
\(\chi_{3332}(33, \cdot)\) |
None |
0 |
12 |
3332.1.ce |
\(\chi_{3332}(31, \cdot)\) |
3332.1.ce.a |
16 |
16 |
3332.1.ce.b |
16 |
3332.1.ce.c |
16 |
3332.1.ce.d |
16 |
3332.1.ch |
\(\chi_{3332}(165, \cdot)\) |
None |
0 |
16 |
3332.1.ci |
\(\chi_{3332}(321, \cdot)\) |
None |
0 |
24 |
3332.1.ck |
\(\chi_{3332}(15, \cdot)\) |
None |
0 |
24 |
3332.1.cm |
\(\chi_{3332}(123, \cdot)\) |
None |
0 |
24 |
3332.1.cp |
\(\chi_{3332}(89, \cdot)\) |
None |
0 |
24 |
3332.1.cr |
\(\chi_{3332}(27, \cdot)\) |
None |
0 |
48 |
3332.1.cs |
\(\chi_{3332}(29, \cdot)\) |
None |
0 |
48 |
3332.1.cv |
\(\chi_{3332}(145, \cdot)\) |
None |
0 |
48 |
3332.1.cx |
\(\chi_{3332}(151, \cdot)\) |
None |
0 |
48 |
3332.1.cz |
\(\chi_{3332}(37, \cdot)\) |
None |
0 |
96 |
3332.1.da |
\(\chi_{3332}(3, \cdot)\) |
None |
0 |
96 |