Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2695))\).
|
Total |
New |
Old |
Modular forms
| 5108 |
2817 |
2291 |
Cusp forms
| 308 |
199 |
109 |
Eisenstein series
| 4800 |
2618 |
2182 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2695))\)
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 |
2695.1.d |
\(\chi_{2695}(736, \cdot)\) |
None |
0 |
1 |
2695.1.e |
\(\chi_{2695}(1959, \cdot)\) |
None |
0 |
1 |
2695.1.f |
\(\chi_{2695}(881, \cdot)\) |
None |
0 |
1 |
2695.1.g |
\(\chi_{2695}(1814, \cdot)\) |
2695.1.g.a |
1 |
1 |
2695.1.g.b |
1 |
2695.1.g.c |
1 |
2695.1.g.d |
1 |
2695.1.g.e |
1 |
2695.1.g.f |
2 |
2695.1.g.g |
2 |
2695.1.g.h |
2 |
2695.1.g.i |
4 |
2695.1.l |
\(\chi_{2695}(538, \cdot)\) |
2695.1.l.a |
8 |
2 |
2695.1.l.b |
8 |
2695.1.m |
\(\chi_{2695}(1618, \cdot)\) |
None |
0 |
2 |
2695.1.p |
\(\chi_{2695}(166, \cdot)\) |
None |
0 |
2 |
2695.1.q |
\(\chi_{2695}(2419, \cdot)\) |
2695.1.q.a |
2 |
2 |
2695.1.q.b |
2 |
2695.1.q.c |
2 |
2695.1.q.d |
2 |
2695.1.q.e |
4 |
2695.1.q.f |
4 |
2695.1.q.g |
8 |
2695.1.r |
\(\chi_{2695}(1341, \cdot)\) |
None |
0 |
2 |
2695.1.s |
\(\chi_{2695}(1244, \cdot)\) |
None |
0 |
2 |
2695.1.x |
\(\chi_{2695}(589, \cdot)\) |
2695.1.x.a |
8 |
4 |
2695.1.y |
\(\chi_{2695}(146, \cdot)\) |
None |
0 |
4 |
2695.1.z |
\(\chi_{2695}(489, \cdot)\) |
None |
0 |
4 |
2695.1.ba |
\(\chi_{2695}(491, \cdot)\) |
None |
0 |
4 |
2695.1.bf |
\(\chi_{2695}(67, \cdot)\) |
None |
0 |
4 |
2695.1.bg |
\(\chi_{2695}(362, \cdot)\) |
2695.1.bg.a |
16 |
4 |
2695.1.bg.b |
16 |
2695.1.bi |
\(\chi_{2695}(274, \cdot)\) |
2695.1.bi.a |
6 |
6 |
2695.1.bi.b |
6 |
2695.1.bi.c |
12 |
2695.1.bj |
\(\chi_{2695}(111, \cdot)\) |
None |
0 |
6 |
2695.1.bk |
\(\chi_{2695}(34, \cdot)\) |
None |
0 |
6 |
2695.1.bl |
\(\chi_{2695}(351, \cdot)\) |
None |
0 |
6 |
2695.1.bp |
\(\chi_{2695}(148, \cdot)\) |
None |
0 |
8 |
2695.1.bq |
\(\chi_{2695}(293, \cdot)\) |
None |
0 |
8 |
2695.1.bu |
\(\chi_{2695}(78, \cdot)\) |
None |
0 |
12 |
2695.1.bv |
\(\chi_{2695}(153, \cdot)\) |
None |
0 |
12 |
2695.1.ca |
\(\chi_{2695}(509, \cdot)\) |
2695.1.ca.a |
8 |
8 |
2695.1.ca.b |
8 |
2695.1.cb |
\(\chi_{2695}(116, \cdot)\) |
None |
0 |
8 |
2695.1.cc |
\(\chi_{2695}(79, \cdot)\) |
2695.1.cc.a |
16 |
8 |
2695.1.cd |
\(\chi_{2695}(31, \cdot)\) |
None |
0 |
8 |
2695.1.ci |
\(\chi_{2695}(89, \cdot)\) |
None |
0 |
12 |
2695.1.cj |
\(\chi_{2695}(186, \cdot)\) |
None |
0 |
12 |
2695.1.ck |
\(\chi_{2695}(109, \cdot)\) |
2695.1.ck.a |
12 |
12 |
2695.1.ck.b |
12 |
2695.1.ck.c |
24 |
2695.1.cl |
\(\chi_{2695}(551, \cdot)\) |
None |
0 |
12 |
2695.1.cn |
\(\chi_{2695}(68, \cdot)\) |
None |
0 |
16 |
2695.1.co |
\(\chi_{2695}(312, \cdot)\) |
None |
0 |
16 |
2695.1.ct |
\(\chi_{2695}(106, \cdot)\) |
None |
0 |
24 |
2695.1.cu |
\(\chi_{2695}(69, \cdot)\) |
None |
0 |
24 |
2695.1.cv |
\(\chi_{2695}(181, \cdot)\) |
None |
0 |
24 |
2695.1.cw |
\(\chi_{2695}(29, \cdot)\) |
None |
0 |
24 |
2695.1.cy |
\(\chi_{2695}(87, \cdot)\) |
None |
0 |
24 |
2695.1.cz |
\(\chi_{2695}(23, \cdot)\) |
None |
0 |
24 |
2695.1.df |
\(\chi_{2695}(13, \cdot)\) |
None |
0 |
48 |
2695.1.dg |
\(\chi_{2695}(92, \cdot)\) |
None |
0 |
48 |
2695.1.di |
\(\chi_{2695}(26, \cdot)\) |
None |
0 |
48 |
2695.1.dj |
\(\chi_{2695}(39, \cdot)\) |
None |
0 |
48 |
2695.1.dk |
\(\chi_{2695}(46, \cdot)\) |
None |
0 |
48 |
2695.1.dl |
\(\chi_{2695}(59, \cdot)\) |
None |
0 |
48 |
2695.1.dq |
\(\chi_{2695}(37, \cdot)\) |
None |
0 |
96 |
2695.1.dr |
\(\chi_{2695}(17, \cdot)\) |
None |
0 |
96 |