Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1232))\).
|
Total |
New |
Old |
Modular forms
| 47760 |
24832 |
22928 |
Cusp forms
| 44401 |
24020 |
20381 |
Eisenstein series
| 3359 |
812 |
2547 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)
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 |
1232.2.a |
\(\chi_{1232}(1, \cdot)\) |
1232.2.a.a |
1 |
1 |
1232.2.a.b |
1 |
1232.2.a.c |
1 |
1232.2.a.d |
1 |
1232.2.a.e |
1 |
1232.2.a.f |
1 |
1232.2.a.g |
1 |
1232.2.a.h |
1 |
1232.2.a.i |
1 |
1232.2.a.j |
1 |
1232.2.a.k |
1 |
1232.2.a.l |
1 |
1232.2.a.m |
2 |
1232.2.a.n |
2 |
1232.2.a.o |
2 |
1232.2.a.p |
2 |
1232.2.a.q |
3 |
1232.2.a.r |
3 |
1232.2.a.s |
4 |
1232.2.c |
\(\chi_{1232}(617, \cdot)\) |
None |
0 |
1 |
1232.2.e |
\(\chi_{1232}(769, \cdot)\) |
1232.2.e.a |
2 |
1 |
1232.2.e.b |
4 |
1232.2.e.c |
4 |
1232.2.e.d |
4 |
1232.2.e.e |
8 |
1232.2.e.f |
24 |
1232.2.f |
\(\chi_{1232}(351, \cdot)\) |
1232.2.f.a |
6 |
1 |
1232.2.f.b |
6 |
1232.2.f.c |
12 |
1232.2.f.d |
12 |
1232.2.h |
\(\chi_{1232}(727, \cdot)\) |
None |
0 |
1 |
1232.2.j |
\(\chi_{1232}(111, \cdot)\) |
1232.2.j.a |
16 |
1 |
1232.2.j.b |
24 |
1232.2.l |
\(\chi_{1232}(967, \cdot)\) |
None |
0 |
1 |
1232.2.o |
\(\chi_{1232}(153, \cdot)\) |
None |
0 |
1 |
1232.2.q |
\(\chi_{1232}(177, \cdot)\) |
1232.2.q.a |
2 |
2 |
1232.2.q.b |
2 |
1232.2.q.c |
2 |
1232.2.q.d |
2 |
1232.2.q.e |
2 |
1232.2.q.f |
4 |
1232.2.q.g |
4 |
1232.2.q.h |
4 |
1232.2.q.i |
6 |
1232.2.q.j |
6 |
1232.2.q.k |
6 |
1232.2.q.l |
6 |
1232.2.q.m |
6 |
1232.2.q.n |
8 |
1232.2.q.o |
10 |
1232.2.q.p |
10 |
1232.2.r |
\(\chi_{1232}(43, \cdot)\) |
n/a |
288 |
2 |
1232.2.s |
\(\chi_{1232}(419, \cdot)\) |
n/a |
320 |
2 |
1232.2.x |
\(\chi_{1232}(461, \cdot)\) |
n/a |
376 |
2 |
1232.2.y |
\(\chi_{1232}(309, \cdot)\) |
n/a |
240 |
2 |
1232.2.z |
\(\chi_{1232}(113, \cdot)\) |
n/a |
144 |
4 |
1232.2.ba |
\(\chi_{1232}(857, \cdot)\) |
None |
0 |
2 |
1232.2.be |
\(\chi_{1232}(815, \cdot)\) |
1232.2.be.a |
24 |
2 |
1232.2.be.b |
28 |
1232.2.be.c |
28 |
1232.2.bg |
\(\chi_{1232}(263, \cdot)\) |
None |
0 |
2 |
1232.2.bi |
\(\chi_{1232}(527, \cdot)\) |
1232.2.bi.a |
32 |
2 |
1232.2.bi.b |
32 |
1232.2.bi.c |
32 |
1232.2.bk |
\(\chi_{1232}(199, \cdot)\) |
None |
0 |
2 |
1232.2.bl |
\(\chi_{1232}(793, \cdot)\) |
None |
0 |
2 |
1232.2.bn |
\(\chi_{1232}(241, \cdot)\) |
1232.2.bn.a |
12 |
2 |
1232.2.bn.b |
16 |
1232.2.bn.c |
16 |
1232.2.bn.d |
48 |
1232.2.bq |
\(\chi_{1232}(41, \cdot)\) |
None |
0 |
4 |
1232.2.bt |
\(\chi_{1232}(183, \cdot)\) |
None |
0 |
4 |
1232.2.bv |
\(\chi_{1232}(223, \cdot)\) |
n/a |
192 |
4 |
1232.2.bx |
\(\chi_{1232}(279, \cdot)\) |
None |
0 |
4 |
1232.2.bz |
\(\chi_{1232}(127, \cdot)\) |
n/a |
144 |
4 |
1232.2.ca |
\(\chi_{1232}(321, \cdot)\) |
n/a |
184 |
4 |
1232.2.cc |
\(\chi_{1232}(169, \cdot)\) |
None |
0 |
4 |
1232.2.cg |
\(\chi_{1232}(243, \cdot)\) |
n/a |
640 |
4 |
1232.2.ch |
\(\chi_{1232}(219, \cdot)\) |
n/a |
752 |
4 |
1232.2.ci |
\(\chi_{1232}(221, \cdot)\) |
n/a |
640 |
4 |
1232.2.cj |
\(\chi_{1232}(285, \cdot)\) |
n/a |
752 |
4 |
1232.2.cm |
\(\chi_{1232}(81, \cdot)\) |
n/a |
368 |
8 |
1232.2.cn |
\(\chi_{1232}(141, \cdot)\) |
n/a |
1152 |
8 |
1232.2.co |
\(\chi_{1232}(13, \cdot)\) |
n/a |
1504 |
8 |
1232.2.ct |
\(\chi_{1232}(27, \cdot)\) |
n/a |
1504 |
8 |
1232.2.cu |
\(\chi_{1232}(211, \cdot)\) |
n/a |
1152 |
8 |
1232.2.cw |
\(\chi_{1232}(17, \cdot)\) |
n/a |
368 |
8 |
1232.2.cy |
\(\chi_{1232}(9, \cdot)\) |
None |
0 |
8 |
1232.2.cz |
\(\chi_{1232}(103, \cdot)\) |
None |
0 |
8 |
1232.2.db |
\(\chi_{1232}(79, \cdot)\) |
n/a |
384 |
8 |
1232.2.dd |
\(\chi_{1232}(39, \cdot)\) |
None |
0 |
8 |
1232.2.df |
\(\chi_{1232}(31, \cdot)\) |
n/a |
384 |
8 |
1232.2.dj |
\(\chi_{1232}(73, \cdot)\) |
None |
0 |
8 |
1232.2.dm |
\(\chi_{1232}(61, \cdot)\) |
n/a |
3008 |
16 |
1232.2.dn |
\(\chi_{1232}(37, \cdot)\) |
n/a |
3008 |
16 |
1232.2.do |
\(\chi_{1232}(51, \cdot)\) |
n/a |
3008 |
16 |
1232.2.dp |
\(\chi_{1232}(3, \cdot)\) |
n/a |
3008 |
16 |
"n/a" means that newforms for that character have not been added to the database yet