Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3328))\).
|
Total |
New |
Old |
Modular forms
| 4568 |
1256 |
3312 |
Cusp forms
| 344 |
112 |
232 |
Eisenstein series
| 4224 |
1144 |
3080 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3328))\)
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 available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
3328.1.c |
\(\chi_{3328}(3327, \cdot)\) |
3328.1.c.a |
2 |
1 |
3328.1.c.b |
2 |
3328.1.c.c |
2 |
3328.1.c.d |
2 |
3328.1.c.e |
2 |
3328.1.c.f |
4 |
3328.1.d |
\(\chi_{3328}(1535, \cdot)\) |
None |
0 |
1 |
3328.1.g |
\(\chi_{3328}(3199, \cdot)\) |
None |
0 |
1 |
3328.1.h |
\(\chi_{3328}(1663, \cdot)\) |
3328.1.h.a |
2 |
1 |
3328.1.j |
\(\chi_{3328}(385, \cdot)\) |
3328.1.j.a |
2 |
2 |
3328.1.j.b |
2 |
3328.1.m |
\(\chi_{3328}(577, \cdot)\) |
3328.1.m.a |
4 |
2 |
3328.1.m.b |
4 |
3328.1.o |
\(\chi_{3328}(831, \cdot)\) |
3328.1.o.a |
4 |
2 |
3328.1.o.b |
4 |
3328.1.o.c |
4 |
3328.1.o.d |
4 |
3328.1.q |
\(\chi_{3328}(703, \cdot)\) |
None |
0 |
2 |
3328.1.r |
\(\chi_{3328}(2241, \cdot)\) |
3328.1.r.a |
4 |
2 |
3328.1.r.b |
4 |
3328.1.t |
\(\chi_{3328}(2049, \cdot)\) |
3328.1.t.a |
2 |
2 |
3328.1.t.b |
2 |
3328.1.t.c |
4 |
3328.1.t.d |
4 |
3328.1.v |
\(\chi_{3328}(1407, \cdot)\) |
3328.1.v.a |
4 |
2 |
3328.1.v.b |
4 |
3328.1.v.c |
4 |
3328.1.x |
\(\chi_{3328}(127, \cdot)\) |
3328.1.x.a |
4 |
2 |
3328.1.y |
\(\chi_{3328}(511, \cdot)\) |
3328.1.y.a |
4 |
2 |
3328.1.bb |
\(\chi_{3328}(1023, \cdot)\) |
3328.1.bb.a |
4 |
2 |
3328.1.bb.b |
4 |
3328.1.bb.c |
4 |
3328.1.bc |
\(\chi_{3328}(801, \cdot)\) |
None |
0 |
4 |
3328.1.be |
\(\chi_{3328}(415, \cdot)\) |
None |
0 |
4 |
3328.1.bh |
\(\chi_{3328}(287, \cdot)\) |
None |
0 |
4 |
3328.1.bj |
\(\chi_{3328}(161, \cdot)\) |
None |
0 |
4 |
3328.1.bl |
\(\chi_{3328}(513, \cdot)\) |
3328.1.bl.a |
4 |
4 |
3328.1.bl.b |
4 |
3328.1.bm |
\(\chi_{3328}(193, \cdot)\) |
None |
0 |
4 |
3328.1.bo |
\(\chi_{3328}(191, \cdot)\) |
None |
0 |
4 |
3328.1.bq |
\(\chi_{3328}(959, \cdot)\) |
None |
0 |
4 |
3328.1.bt |
\(\chi_{3328}(1857, \cdot)\) |
None |
0 |
4 |
3328.1.bv |
\(\chi_{3328}(2177, \cdot)\) |
3328.1.bv.a |
4 |
4 |
3328.1.bv.b |
4 |
3328.1.bx |
\(\chi_{3328}(177, \cdot)\) |
None |
0 |
8 |
3328.1.bz |
\(\chi_{3328}(207, \cdot)\) |
None |
0 |
8 |
3328.1.ca |
\(\chi_{3328}(79, \cdot)\) |
None |
0 |
8 |
3328.1.cd |
\(\chi_{3328}(369, \cdot)\) |
None |
0 |
8 |
3328.1.ce |
\(\chi_{3328}(609, \cdot)\) |
None |
0 |
8 |
3328.1.cg |
\(\chi_{3328}(159, \cdot)\) |
None |
0 |
8 |
3328.1.cj |
\(\chi_{3328}(95, \cdot)\) |
None |
0 |
8 |
3328.1.cl |
\(\chi_{3328}(33, \cdot)\) |
None |
0 |
8 |
3328.1.cm |
\(\chi_{3328}(265, \cdot)\) |
None |
0 |
16 |
3328.1.co |
\(\chi_{3328}(103, \cdot)\) |
None |
0 |
16 |
3328.1.cq |
\(\chi_{3328}(183, \cdot)\) |
None |
0 |
16 |
3328.1.ct |
\(\chi_{3328}(57, \cdot)\) |
None |
0 |
16 |
3328.1.cu |
\(\chi_{3328}(305, \cdot)\) |
None |
0 |
16 |
3328.1.cw |
\(\chi_{3328}(303, \cdot)\) |
None |
0 |
16 |
3328.1.cz |
\(\chi_{3328}(367, \cdot)\) |
None |
0 |
16 |
3328.1.da |
\(\chi_{3328}(145, \cdot)\) |
None |
0 |
16 |
3328.1.dd |
\(\chi_{3328}(5, \cdot)\) |
None |
0 |
32 |
3328.1.dg |
\(\chi_{3328}(27, \cdot)\) |
None |
0 |
32 |
3328.1.dh |
\(\chi_{3328}(51, \cdot)\) |
None |
0 |
32 |
3328.1.dj |
\(\chi_{3328}(21, \cdot)\) |
None |
0 |
32 |
3328.1.dl |
\(\chi_{3328}(41, \cdot)\) |
None |
0 |
32 |
3328.1.dn |
\(\chi_{3328}(55, \cdot)\) |
None |
0 |
32 |
3328.1.dp |
\(\chi_{3328}(23, \cdot)\) |
None |
0 |
32 |
3328.1.dq |
\(\chi_{3328}(137, \cdot)\) |
None |
0 |
32 |
3328.1.ds |
\(\chi_{3328}(37, \cdot)\) |
None |
0 |
64 |
3328.1.du |
\(\chi_{3328}(3, \cdot)\) |
None |
0 |
64 |
3328.1.dv |
\(\chi_{3328}(43, \cdot)\) |
None |
0 |
64 |
3328.1.dy |
\(\chi_{3328}(141, \cdot)\) |
None |
0 |
64 |