Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1368))\).
|
Total |
New |
Old |
Modular forms
| 2032 |
416 |
1616 |
Cusp forms
| 304 |
110 |
194 |
Eisenstein series
| 1728 |
306 |
1422 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1368))\)
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 |
1368.1.b |
\(\chi_{1368}(1367, \cdot)\) |
None |
0 |
1 |
1368.1.c |
\(\chi_{1368}(1027, \cdot)\) |
None |
0 |
1 |
1368.1.h |
\(\chi_{1368}(305, \cdot)\) |
None |
0 |
1 |
1368.1.i |
\(\chi_{1368}(37, \cdot)\) |
1368.1.i.a |
1 |
1 |
1368.1.i.b |
1 |
1368.1.l |
\(\chi_{1368}(683, \cdot)\) |
1368.1.l.a |
4 |
1 |
1368.1.m |
\(\chi_{1368}(343, \cdot)\) |
None |
0 |
1 |
1368.1.n |
\(\chi_{1368}(989, \cdot)\) |
None |
0 |
1 |
1368.1.o |
\(\chi_{1368}(721, \cdot)\) |
None |
0 |
1 |
1368.1.u |
\(\chi_{1368}(373, \cdot)\) |
None |
0 |
2 |
1368.1.v |
\(\chi_{1368}(353, \cdot)\) |
None |
0 |
2 |
1368.1.ba |
\(\chi_{1368}(619, \cdot)\) |
1368.1.ba.a |
2 |
2 |
1368.1.ba.b |
2 |
1368.1.ba.c |
4 |
1368.1.bb |
\(\chi_{1368}(407, \cdot)\) |
None |
0 |
2 |
1368.1.bc |
\(\chi_{1368}(847, \cdot)\) |
None |
0 |
2 |
1368.1.bd |
\(\chi_{1368}(107, \cdot)\) |
None |
0 |
2 |
1368.1.bg |
\(\chi_{1368}(601, \cdot)\) |
None |
0 |
2 |
1368.1.bh |
\(\chi_{1368}(581, \cdot)\) |
None |
0 |
2 |
1368.1.bj |
\(\chi_{1368}(77, \cdot)\) |
None |
0 |
2 |
1368.1.bk |
\(\chi_{1368}(265, \cdot)\) |
None |
0 |
2 |
1368.1.bo |
\(\chi_{1368}(227, \cdot)\) |
1368.1.bo.a |
2 |
2 |
1368.1.bo.b |
2 |
1368.1.bp |
\(\chi_{1368}(799, \cdot)\) |
None |
0 |
2 |
1368.1.bs |
\(\chi_{1368}(7, \cdot)\) |
None |
0 |
2 |
1368.1.bt |
\(\chi_{1368}(635, \cdot)\) |
1368.1.bt.a |
2 |
2 |
1368.1.bt.b |
2 |
1368.1.bv |
\(\chi_{1368}(145, \cdot)\) |
None |
0 |
2 |
1368.1.bw |
\(\chi_{1368}(125, \cdot)\) |
1368.1.bw.a |
8 |
2 |
1368.1.bz |
\(\chi_{1368}(163, \cdot)\) |
1368.1.bz.a |
2 |
2 |
1368.1.ca |
\(\chi_{1368}(791, \cdot)\) |
None |
0 |
2 |
1368.1.cd |
\(\chi_{1368}(761, \cdot)\) |
None |
0 |
2 |
1368.1.ce |
\(\chi_{1368}(493, \cdot)\) |
1368.1.ce.a |
6 |
2 |
1368.1.ce.b |
6 |
1368.1.ch |
\(\chi_{1368}(445, \cdot)\) |
None |
0 |
2 |
1368.1.ci |
\(\chi_{1368}(425, \cdot)\) |
None |
0 |
2 |
1368.1.cj |
\(\chi_{1368}(691, \cdot)\) |
1368.1.cj.a |
2 |
2 |
1368.1.cj.b |
2 |
1368.1.cj.c |
4 |
1368.1.ck |
\(\chi_{1368}(335, \cdot)\) |
None |
0 |
2 |
1368.1.cn |
\(\chi_{1368}(455, \cdot)\) |
None |
0 |
2 |
1368.1.co |
\(\chi_{1368}(115, \cdot)\) |
None |
0 |
2 |
1368.1.cr |
\(\chi_{1368}(829, \cdot)\) |
None |
0 |
2 |
1368.1.cs |
\(\chi_{1368}(809, \cdot)\) |
None |
0 |
2 |
1368.1.cw |
\(\chi_{1368}(673, \cdot)\) |
None |
0 |
2 |
1368.1.cx |
\(\chi_{1368}(653, \cdot)\) |
None |
0 |
2 |
1368.1.cy |
\(\chi_{1368}(463, \cdot)\) |
None |
0 |
2 |
1368.1.cz |
\(\chi_{1368}(563, \cdot)\) |
1368.1.cz.a |
2 |
2 |
1368.1.cz.b |
2 |
1368.1.df |
\(\chi_{1368}(167, \cdot)\) |
None |
0 |
6 |
1368.1.dh |
\(\chi_{1368}(43, \cdot)\) |
1368.1.dh.a |
6 |
6 |
1368.1.dh.b |
6 |
1368.1.dk |
\(\chi_{1368}(155, \cdot)\) |
1368.1.dk.a |
6 |
6 |
1368.1.dk.b |
6 |
1368.1.dm |
\(\chi_{1368}(175, \cdot)\) |
None |
0 |
6 |
1368.1.do |
\(\chi_{1368}(205, \cdot)\) |
None |
0 |
6 |
1368.1.dq |
\(\chi_{1368}(137, \cdot)\) |
None |
0 |
6 |
1368.1.dr |
\(\chi_{1368}(557, \cdot)\) |
None |
0 |
6 |
1368.1.ds |
\(\chi_{1368}(433, \cdot)\) |
None |
0 |
6 |
1368.1.dv |
\(\chi_{1368}(17, \cdot)\) |
None |
0 |
6 |
1368.1.dx |
\(\chi_{1368}(109, \cdot)\) |
None |
0 |
6 |
1368.1.dy |
\(\chi_{1368}(193, \cdot)\) |
None |
0 |
6 |
1368.1.ea |
\(\chi_{1368}(5, \cdot)\) |
None |
0 |
6 |
1368.1.ec |
\(\chi_{1368}(367, \cdot)\) |
None |
0 |
6 |
1368.1.ee |
\(\chi_{1368}(59, \cdot)\) |
1368.1.ee.a |
6 |
6 |
1368.1.ee.b |
6 |
1368.1.ef |
\(\chi_{1368}(71, \cdot)\) |
None |
0 |
6 |
1368.1.eh |
\(\chi_{1368}(595, \cdot)\) |
1368.1.eh.a |
6 |
6 |
1368.1.ek |
\(\chi_{1368}(395, \cdot)\) |
None |
0 |
6 |
1368.1.em |
\(\chi_{1368}(55, \cdot)\) |
None |
0 |
6 |
1368.1.en |
\(\chi_{1368}(283, \cdot)\) |
1368.1.en.a |
6 |
6 |
1368.1.en.b |
6 |
1368.1.ep |
\(\chi_{1368}(383, \cdot)\) |
None |
0 |
6 |
1368.1.er |
\(\chi_{1368}(245, \cdot)\) |
None |
0 |
6 |
1368.1.es |
\(\chi_{1368}(97, \cdot)\) |
None |
0 |
6 |
1368.1.ev |
\(\chi_{1368}(329, \cdot)\) |
None |
0 |
6 |
1368.1.ex |
\(\chi_{1368}(13, \cdot)\) |
None |
0 |
6 |