Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1088))\).
|
Total |
New |
Old |
Modular forms
| 111744 |
62106 |
49638 |
Cusp forms
| 109440 |
61446 |
47994 |
Eisenstein series
| 2304 |
660 |
1644 |
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1088))\)
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 available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
1088.4.a |
\(\chi_{1088}(1, \cdot)\) |
1088.4.a.a |
1 |
1 |
1088.4.a.b |
1 |
1088.4.a.c |
1 |
1088.4.a.d |
1 |
1088.4.a.e |
1 |
1088.4.a.f |
1 |
1088.4.a.g |
1 |
1088.4.a.h |
1 |
1088.4.a.i |
1 |
1088.4.a.j |
1 |
1088.4.a.k |
1 |
1088.4.a.l |
1 |
1088.4.a.m |
2 |
1088.4.a.n |
2 |
1088.4.a.o |
2 |
1088.4.a.p |
2 |
1088.4.a.q |
2 |
1088.4.a.r |
3 |
1088.4.a.s |
3 |
1088.4.a.t |
3 |
1088.4.a.u |
3 |
1088.4.a.v |
3 |
1088.4.a.w |
3 |
1088.4.a.x |
3 |
1088.4.a.y |
3 |
1088.4.a.z |
3 |
1088.4.a.ba |
3 |
1088.4.a.bb |
4 |
1088.4.a.bc |
4 |
1088.4.a.bd |
4 |
1088.4.a.be |
4 |
1088.4.a.bf |
6 |
1088.4.a.bg |
7 |
1088.4.a.bh |
7 |
1088.4.a.bi |
8 |
1088.4.b |
\(\chi_{1088}(577, \cdot)\) |
n/a |
106 |
1 |
1088.4.c |
\(\chi_{1088}(545, \cdot)\) |
1088.4.c.a |
16 |
1 |
1088.4.c.b |
16 |
1088.4.c.c |
32 |
1088.4.c.d |
32 |
1088.4.h |
\(\chi_{1088}(33, \cdot)\) |
n/a |
108 |
1 |
1088.4.j |
\(\chi_{1088}(81, \cdot)\) |
n/a |
212 |
2 |
1088.4.l |
\(\chi_{1088}(273, \cdot)\) |
n/a |
192 |
2 |
1088.4.m |
\(\chi_{1088}(225, \cdot)\) |
n/a |
216 |
2 |
1088.4.o |
\(\chi_{1088}(769, \cdot)\) |
n/a |
212 |
2 |
1088.4.r |
\(\chi_{1088}(305, \cdot)\) |
n/a |
212 |
2 |
1088.4.s |
\(\chi_{1088}(625, \cdot)\) |
n/a |
212 |
2 |
1088.4.v |
\(\chi_{1088}(281, \cdot)\) |
None |
0 |
4 |
1088.4.x |
\(\chi_{1088}(185, \cdot)\) |
None |
0 |
4 |
1088.4.z |
\(\chi_{1088}(89, \cdot)\) |
None |
0 |
4 |
1088.4.bb |
\(\chi_{1088}(257, \cdot)\) |
n/a |
424 |
4 |
1088.4.bc |
\(\chi_{1088}(169, \cdot)\) |
None |
0 |
4 |
1088.4.bd |
\(\chi_{1088}(137, \cdot)\) |
None |
0 |
4 |
1088.4.be |
\(\chi_{1088}(433, \cdot)\) |
n/a |
424 |
4 |
1088.4.bg |
\(\chi_{1088}(49, \cdot)\) |
n/a |
424 |
4 |
1088.4.bk |
\(\chi_{1088}(161, \cdot)\) |
n/a |
432 |
4 |
1088.4.bn |
\(\chi_{1088}(217, \cdot)\) |
None |
0 |
4 |
1088.4.bp |
\(\chi_{1088}(9, \cdot)\) |
None |
0 |
4 |
1088.4.bq |
\(\chi_{1088}(25, \cdot)\) |
None |
0 |
4 |
1088.4.bs |
\(\chi_{1088}(139, \cdot)\) |
n/a |
3440 |
8 |
1088.4.bv |
\(\chi_{1088}(3, \cdot)\) |
n/a |
3440 |
8 |
1088.4.bx |
\(\chi_{1088}(189, \cdot)\) |
n/a |
3440 |
8 |
1088.4.by |
\(\chi_{1088}(147, \cdot)\) |
n/a |
3440 |
8 |
1088.4.ca |
\(\chi_{1088}(107, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cd |
\(\chi_{1088}(79, \cdot)\) |
n/a |
848 |
8 |
1088.4.ce |
\(\chi_{1088}(53, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cf |
\(\chi_{1088}(77, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cg |
\(\chi_{1088}(7, \cdot)\) |
None |
0 |
8 |
1088.4.cj |
\(\chi_{1088}(75, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cl |
\(\chi_{1088}(91, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cn |
\(\chi_{1088}(69, \cdot)\) |
n/a |
3072 |
8 |
1088.4.cp |
\(\chi_{1088}(63, \cdot)\) |
n/a |
848 |
8 |
1088.4.cr |
\(\chi_{1088}(23, \cdot)\) |
None |
0 |
8 |
1088.4.cs |
\(\chi_{1088}(13, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cv |
\(\chi_{1088}(149, \cdot)\) |
n/a |
3440 |
8 |
1088.4.cx |
\(\chi_{1088}(39, \cdot)\) |
None |
0 |
8 |
1088.4.cy |
\(\chi_{1088}(31, \cdot)\) |
n/a |
864 |
8 |
1088.4.da |
\(\chi_{1088}(101, \cdot)\) |
n/a |
3440 |
8 |
1088.4.dc |
\(\chi_{1088}(231, \cdot)\) |
None |
0 |
8 |
1088.4.dh |
\(\chi_{1088}(207, \cdot)\) |
n/a |
848 |
8 |
1088.4.dj |
\(\chi_{1088}(253, \cdot)\) |
n/a |
3440 |
8 |
1088.4.dl |
\(\chi_{1088}(347, \cdot)\) |
n/a |
3440 |
8 |
1088.4.dm |
\(\chi_{1088}(379, \cdot)\) |
n/a |
3440 |
8 |
"n/a" means that newforms for that character have not been added to the database yet