Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1287))\).
|
Total |
New |
Old |
Modular forms
| 62400 |
47414 |
14986 |
Cusp forms
| 58561 |
45630 |
12931 |
Eisenstein series
| 3839 |
1784 |
2055 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1287))\)
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 |
1287.2.a |
\(\chi_{1287}(1, \cdot)\) |
1287.2.a.a |
1 |
1 |
1287.2.a.b |
1 |
1287.2.a.c |
1 |
1287.2.a.d |
1 |
1287.2.a.e |
1 |
1287.2.a.f |
2 |
1287.2.a.g |
2 |
1287.2.a.h |
3 |
1287.2.a.i |
3 |
1287.2.a.j |
3 |
1287.2.a.k |
4 |
1287.2.a.l |
4 |
1287.2.a.m |
4 |
1287.2.a.n |
4 |
1287.2.a.o |
5 |
1287.2.a.p |
5 |
1287.2.a.q |
6 |
1287.2.b |
\(\chi_{1287}(298, \cdot)\) |
1287.2.b.a |
10 |
1 |
1287.2.b.b |
12 |
1287.2.b.c |
14 |
1287.2.b.d |
20 |
1287.2.e |
\(\chi_{1287}(1286, \cdot)\) |
1287.2.e.a |
4 |
1 |
1287.2.e.b |
4 |
1287.2.e.c |
4 |
1287.2.e.d |
4 |
1287.2.e.e |
40 |
1287.2.f |
\(\chi_{1287}(989, \cdot)\) |
1287.2.f.a |
48 |
1 |
1287.2.i |
\(\chi_{1287}(430, \cdot)\) |
n/a |
240 |
2 |
1287.2.j |
\(\chi_{1287}(529, \cdot)\) |
n/a |
280 |
2 |
1287.2.k |
\(\chi_{1287}(100, \cdot)\) |
n/a |
120 |
2 |
1287.2.l |
\(\chi_{1287}(133, \cdot)\) |
n/a |
280 |
2 |
1287.2.m |
\(\chi_{1287}(980, \cdot)\) |
1287.2.m.a |
4 |
2 |
1287.2.m.b |
40 |
1287.2.m.c |
44 |
1287.2.p |
\(\chi_{1287}(109, \cdot)\) |
n/a |
136 |
2 |
1287.2.q |
\(\chi_{1287}(235, \cdot)\) |
n/a |
240 |
4 |
1287.2.r |
\(\chi_{1287}(329, \cdot)\) |
n/a |
328 |
2 |
1287.2.u |
\(\chi_{1287}(1024, \cdot)\) |
n/a |
280 |
2 |
1287.2.w |
\(\chi_{1287}(692, \cdot)\) |
n/a |
112 |
2 |
1287.2.z |
\(\chi_{1287}(659, \cdot)\) |
n/a |
328 |
2 |
1287.2.bb |
\(\chi_{1287}(131, \cdot)\) |
n/a |
288 |
2 |
1287.2.bf |
\(\chi_{1287}(199, \cdot)\) |
n/a |
116 |
2 |
1287.2.bh |
\(\chi_{1287}(428, \cdot)\) |
n/a |
328 |
2 |
1287.2.bj |
\(\chi_{1287}(725, \cdot)\) |
n/a |
328 |
2 |
1287.2.bk |
\(\chi_{1287}(166, \cdot)\) |
n/a |
280 |
2 |
1287.2.bm |
\(\chi_{1287}(727, \cdot)\) |
n/a |
280 |
2 |
1287.2.bo |
\(\chi_{1287}(296, \cdot)\) |
n/a |
112 |
2 |
1287.2.bs |
\(\chi_{1287}(230, \cdot)\) |
n/a |
328 |
2 |
1287.2.bv |
\(\chi_{1287}(404, \cdot)\) |
n/a |
192 |
4 |
1287.2.bw |
\(\chi_{1287}(116, \cdot)\) |
n/a |
224 |
4 |
1287.2.bz |
\(\chi_{1287}(64, \cdot)\) |
n/a |
272 |
4 |
1287.2.ca |
\(\chi_{1287}(175, \cdot)\) |
n/a |
656 |
4 |
1287.2.cd |
\(\chi_{1287}(353, \cdot)\) |
n/a |
560 |
4 |
1287.2.cf |
\(\chi_{1287}(122, \cdot)\) |
n/a |
560 |
4 |
1287.2.ch |
\(\chi_{1287}(76, \cdot)\) |
n/a |
656 |
4 |
1287.2.cj |
\(\chi_{1287}(505, \cdot)\) |
n/a |
272 |
4 |
1287.2.ck |
\(\chi_{1287}(89, \cdot)\) |
n/a |
192 |
4 |
1287.2.cm |
\(\chi_{1287}(254, \cdot)\) |
n/a |
560 |
4 |
1287.2.co |
\(\chi_{1287}(538, \cdot)\) |
n/a |
656 |
4 |
1287.2.cq |
\(\chi_{1287}(16, \cdot)\) |
n/a |
1312 |
8 |
1287.2.cr |
\(\chi_{1287}(289, \cdot)\) |
n/a |
544 |
8 |
1287.2.cs |
\(\chi_{1287}(295, \cdot)\) |
n/a |
1312 |
8 |
1287.2.ct |
\(\chi_{1287}(157, \cdot)\) |
n/a |
1152 |
8 |
1287.2.cv |
\(\chi_{1287}(125, \cdot)\) |
n/a |
448 |
8 |
1287.2.cw |
\(\chi_{1287}(73, \cdot)\) |
n/a |
544 |
8 |
1287.2.cy |
\(\chi_{1287}(29, \cdot)\) |
n/a |
1312 |
8 |
1287.2.dc |
\(\chi_{1287}(17, \cdot)\) |
n/a |
448 |
8 |
1287.2.de |
\(\chi_{1287}(25, \cdot)\) |
n/a |
1312 |
8 |
1287.2.dg |
\(\chi_{1287}(49, \cdot)\) |
n/a |
1312 |
8 |
1287.2.dh |
\(\chi_{1287}(140, \cdot)\) |
n/a |
1312 |
8 |
1287.2.dj |
\(\chi_{1287}(194, \cdot)\) |
n/a |
1312 |
8 |
1287.2.dl |
\(\chi_{1287}(82, \cdot)\) |
n/a |
544 |
8 |
1287.2.dp |
\(\chi_{1287}(248, \cdot)\) |
n/a |
1152 |
8 |
1287.2.dr |
\(\chi_{1287}(68, \cdot)\) |
n/a |
1312 |
8 |
1287.2.du |
\(\chi_{1287}(35, \cdot)\) |
n/a |
448 |
8 |
1287.2.dw |
\(\chi_{1287}(4, \cdot)\) |
n/a |
1312 |
8 |
1287.2.dz |
\(\chi_{1287}(95, \cdot)\) |
n/a |
1312 |
8 |
1287.2.ea |
\(\chi_{1287}(5, \cdot)\) |
n/a |
2624 |
16 |
1287.2.ec |
\(\chi_{1287}(19, \cdot)\) |
n/a |
1088 |
16 |
1287.2.ee |
\(\chi_{1287}(7, \cdot)\) |
n/a |
2624 |
16 |
1287.2.eh |
\(\chi_{1287}(20, \cdot)\) |
n/a |
2624 |
16 |
1287.2.ej |
\(\chi_{1287}(71, \cdot)\) |
n/a |
896 |
16 |
1287.2.el |
\(\chi_{1287}(112, \cdot)\) |
n/a |
2624 |
16 |
1287.2.en |
\(\chi_{1287}(85, \cdot)\) |
n/a |
2624 |
16 |
1287.2.eo |
\(\chi_{1287}(59, \cdot)\) |
n/a |
2624 |
16 |
"n/a" means that newforms for that character have not been added to the database yet