Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1395))\).
|
Total |
New |
Old |
Modular forms
| 71040 |
50840 |
20200 |
Cusp forms
| 67201 |
49272 |
17929 |
Eisenstein series
| 3839 |
1568 |
2271 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1395))\)
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 |
1395.2.a |
\(\chi_{1395}(1, \cdot)\) |
1395.2.a.a |
1 |
1 |
1395.2.a.b |
1 |
1395.2.a.c |
1 |
1395.2.a.d |
1 |
1395.2.a.e |
1 |
1395.2.a.f |
2 |
1395.2.a.g |
2 |
1395.2.a.h |
3 |
1395.2.a.i |
3 |
1395.2.a.j |
3 |
1395.2.a.k |
4 |
1395.2.a.l |
4 |
1395.2.a.m |
4 |
1395.2.a.n |
5 |
1395.2.a.o |
5 |
1395.2.a.p |
5 |
1395.2.a.q |
5 |
1395.2.c |
\(\chi_{1395}(559, \cdot)\) |
1395.2.c.a |
2 |
1 |
1395.2.c.b |
2 |
1395.2.c.c |
4 |
1395.2.c.d |
8 |
1395.2.c.e |
10 |
1395.2.c.f |
10 |
1395.2.c.g |
16 |
1395.2.c.h |
22 |
1395.2.e |
\(\chi_{1395}(836, \cdot)\) |
1395.2.e.a |
40 |
1 |
1395.2.g |
\(\chi_{1395}(1394, \cdot)\) |
1395.2.g.a |
24 |
1 |
1395.2.g.b |
40 |
1395.2.i |
\(\chi_{1395}(466, \cdot)\) |
n/a |
240 |
2 |
1395.2.j |
\(\chi_{1395}(211, \cdot)\) |
n/a |
256 |
2 |
1395.2.k |
\(\chi_{1395}(346, \cdot)\) |
n/a |
256 |
2 |
1395.2.l |
\(\chi_{1395}(676, \cdot)\) |
n/a |
108 |
2 |
1395.2.m |
\(\chi_{1395}(433, \cdot)\) |
n/a |
156 |
2 |
1395.2.n |
\(\chi_{1395}(683, \cdot)\) |
n/a |
120 |
2 |
1395.2.q |
\(\chi_{1395}(721, \cdot)\) |
n/a |
208 |
4 |
1395.2.r |
\(\chi_{1395}(26, \cdot)\) |
1395.2.r.a |
88 |
2 |
1395.2.t |
\(\chi_{1395}(1234, \cdot)\) |
n/a |
156 |
2 |
1395.2.v |
\(\chi_{1395}(254, \cdot)\) |
n/a |
376 |
2 |
1395.2.ba |
\(\chi_{1395}(464, \cdot)\) |
n/a |
376 |
2 |
1395.2.bc |
\(\chi_{1395}(119, \cdot)\) |
n/a |
376 |
2 |
1395.2.be |
\(\chi_{1395}(304, \cdot)\) |
n/a |
376 |
2 |
1395.2.bh |
\(\chi_{1395}(371, \cdot)\) |
n/a |
256 |
2 |
1395.2.bj |
\(\chi_{1395}(626, \cdot)\) |
n/a |
256 |
2 |
1395.2.bl |
\(\chi_{1395}(94, \cdot)\) |
n/a |
360 |
2 |
1395.2.bn |
\(\chi_{1395}(439, \cdot)\) |
n/a |
376 |
2 |
1395.2.bo |
\(\chi_{1395}(491, \cdot)\) |
n/a |
256 |
2 |
1395.2.br |
\(\chi_{1395}(584, \cdot)\) |
n/a |
128 |
2 |
1395.2.bu |
\(\chi_{1395}(89, \cdot)\) |
n/a |
256 |
4 |
1395.2.bw |
\(\chi_{1395}(116, \cdot)\) |
n/a |
160 |
4 |
1395.2.by |
\(\chi_{1395}(64, \cdot)\) |
n/a |
312 |
4 |
1395.2.cc |
\(\chi_{1395}(98, \cdot)\) |
n/a |
256 |
4 |
1395.2.cd |
\(\chi_{1395}(37, \cdot)\) |
n/a |
312 |
4 |
1395.2.ce |
\(\chi_{1395}(88, \cdot)\) |
n/a |
752 |
4 |
1395.2.cf |
\(\chi_{1395}(428, \cdot)\) |
n/a |
752 |
4 |
1395.2.ck |
\(\chi_{1395}(32, \cdot)\) |
n/a |
720 |
4 |
1395.2.cl |
\(\chi_{1395}(563, \cdot)\) |
n/a |
752 |
4 |
1395.2.cm |
\(\chi_{1395}(247, \cdot)\) |
n/a |
752 |
4 |
1395.2.cn |
\(\chi_{1395}(223, \cdot)\) |
n/a |
752 |
4 |
1395.2.cq |
\(\chi_{1395}(226, \cdot)\) |
n/a |
432 |
8 |
1395.2.cr |
\(\chi_{1395}(286, \cdot)\) |
n/a |
1024 |
8 |
1395.2.cs |
\(\chi_{1395}(76, \cdot)\) |
n/a |
1024 |
8 |
1395.2.ct |
\(\chi_{1395}(16, \cdot)\) |
n/a |
1024 |
8 |
1395.2.cw |
\(\chi_{1395}(8, \cdot)\) |
n/a |
512 |
8 |
1395.2.cx |
\(\chi_{1395}(523, \cdot)\) |
n/a |
624 |
8 |
1395.2.cz |
\(\chi_{1395}(44, \cdot)\) |
n/a |
512 |
8 |
1395.2.dc |
\(\chi_{1395}(176, \cdot)\) |
n/a |
1024 |
8 |
1395.2.dd |
\(\chi_{1395}(634, \cdot)\) |
n/a |
1504 |
8 |
1395.2.df |
\(\chi_{1395}(4, \cdot)\) |
n/a |
1504 |
8 |
1395.2.dh |
\(\chi_{1395}(11, \cdot)\) |
n/a |
1024 |
8 |
1395.2.dj |
\(\chi_{1395}(356, \cdot)\) |
n/a |
1024 |
8 |
1395.2.dm |
\(\chi_{1395}(49, \cdot)\) |
n/a |
1504 |
8 |
1395.2.do |
\(\chi_{1395}(569, \cdot)\) |
n/a |
1504 |
8 |
1395.2.dq |
\(\chi_{1395}(29, \cdot)\) |
n/a |
1504 |
8 |
1395.2.dv |
\(\chi_{1395}(74, \cdot)\) |
n/a |
1504 |
8 |
1395.2.dx |
\(\chi_{1395}(19, \cdot)\) |
n/a |
624 |
8 |
1395.2.dz |
\(\chi_{1395}(251, \cdot)\) |
n/a |
352 |
8 |
1395.2.ec |
\(\chi_{1395}(13, \cdot)\) |
n/a |
3008 |
16 |
1395.2.ed |
\(\chi_{1395}(58, \cdot)\) |
n/a |
3008 |
16 |
1395.2.ee |
\(\chi_{1395}(38, \cdot)\) |
n/a |
3008 |
16 |
1395.2.ef |
\(\chi_{1395}(2, \cdot)\) |
n/a |
3008 |
16 |
1395.2.ek |
\(\chi_{1395}(173, \cdot)\) |
n/a |
3008 |
16 |
1395.2.el |
\(\chi_{1395}(52, \cdot)\) |
n/a |
3008 |
16 |
1395.2.em |
\(\chi_{1395}(73, \cdot)\) |
n/a |
1248 |
16 |
1395.2.en |
\(\chi_{1395}(107, \cdot)\) |
n/a |
1024 |
16 |
"n/a" means that newforms for that character have not been added to the database yet