Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3015))\).
|
Total |
New |
Old |
Modular forms
| 327360 |
236150 |
91210 |
Cusp forms
| 318913 |
232638 |
86275 |
Eisenstein series
| 8447 |
3512 |
4935 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3015))\)
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 |
3015.2.a |
\(\chi_{3015}(1, \cdot)\) |
3015.2.a.a |
1 |
1 |
3015.2.a.b |
1 |
3015.2.a.c |
1 |
3015.2.a.d |
2 |
3015.2.a.e |
2 |
3015.2.a.f |
4 |
3015.2.a.g |
4 |
3015.2.a.h |
4 |
3015.2.a.i |
4 |
3015.2.a.j |
5 |
3015.2.a.k |
5 |
3015.2.a.l |
7 |
3015.2.a.m |
7 |
3015.2.a.n |
8 |
3015.2.a.o |
9 |
3015.2.a.p |
9 |
3015.2.a.q |
11 |
3015.2.a.r |
13 |
3015.2.a.s |
13 |
3015.2.c |
\(\chi_{3015}(604, \cdot)\) |
n/a |
164 |
1 |
3015.2.e |
\(\chi_{3015}(3014, \cdot)\) |
n/a |
136 |
1 |
3015.2.g |
\(\chi_{3015}(2411, \cdot)\) |
3015.2.g.a |
4 |
1 |
3015.2.g.b |
4 |
3015.2.g.c |
40 |
3015.2.g.d |
40 |
3015.2.i |
\(\chi_{3015}(1006, \cdot)\) |
n/a |
528 |
2 |
3015.2.j |
\(\chi_{3015}(766, \cdot)\) |
n/a |
228 |
2 |
3015.2.k |
\(\chi_{3015}(841, \cdot)\) |
n/a |
544 |
2 |
3015.2.l |
\(\chi_{3015}(2776, \cdot)\) |
n/a |
544 |
2 |
3015.2.m |
\(\chi_{3015}(937, \cdot)\) |
n/a |
336 |
2 |
3015.2.n |
\(\chi_{3015}(872, \cdot)\) |
n/a |
264 |
2 |
3015.2.q |
\(\chi_{3015}(164, \cdot)\) |
n/a |
808 |
2 |
3015.2.s |
\(\chi_{3015}(364, \cdot)\) |
n/a |
808 |
2 |
3015.2.v |
\(\chi_{3015}(641, \cdot)\) |
n/a |
544 |
2 |
3015.2.y |
\(\chi_{3015}(566, \cdot)\) |
n/a |
184 |
2 |
3015.2.z |
\(\chi_{3015}(401, \cdot)\) |
n/a |
544 |
2 |
3015.2.be |
\(\chi_{3015}(1444, \cdot)\) |
n/a |
808 |
2 |
3015.2.bf |
\(\chi_{3015}(1169, \cdot)\) |
n/a |
272 |
2 |
3015.2.bg |
\(\chi_{3015}(1004, \cdot)\) |
n/a |
808 |
2 |
3015.2.bj |
\(\chi_{3015}(1609, \cdot)\) |
n/a |
792 |
2 |
3015.2.bk |
\(\chi_{3015}(1369, \cdot)\) |
n/a |
336 |
2 |
3015.2.bo |
\(\chi_{3015}(1244, \cdot)\) |
n/a |
808 |
2 |
3015.2.bq |
\(\chi_{3015}(2576, \cdot)\) |
n/a |
544 |
2 |
3015.2.bs |
\(\chi_{3015}(91, \cdot)\) |
n/a |
1120 |
10 |
3015.2.bv |
\(\chi_{3015}(833, \cdot)\) |
n/a |
1616 |
4 |
3015.2.bw |
\(\chi_{3015}(97, \cdot)\) |
n/a |
1616 |
4 |
3015.2.bx |
\(\chi_{3015}(632, \cdot)\) |
n/a |
1616 |
4 |
3015.2.by |
\(\chi_{3015}(1102, \cdot)\) |
n/a |
1616 |
4 |
3015.2.cd |
\(\chi_{3015}(172, \cdot)\) |
n/a |
672 |
4 |
3015.2.ce |
\(\chi_{3015}(68, \cdot)\) |
n/a |
1584 |
4 |
3015.2.cf |
\(\chi_{3015}(133, \cdot)\) |
n/a |
1616 |
4 |
3015.2.cg |
\(\chi_{3015}(908, \cdot)\) |
n/a |
544 |
4 |
3015.2.ck |
\(\chi_{3015}(161, \cdot)\) |
n/a |
880 |
10 |
3015.2.cm |
\(\chi_{3015}(179, \cdot)\) |
n/a |
1360 |
10 |
3015.2.co |
\(\chi_{3015}(64, \cdot)\) |
n/a |
1680 |
10 |
3015.2.cq |
\(\chi_{3015}(16, \cdot)\) |
n/a |
5440 |
20 |
3015.2.cr |
\(\chi_{3015}(121, \cdot)\) |
n/a |
5440 |
20 |
3015.2.cs |
\(\chi_{3015}(181, \cdot)\) |
n/a |
2280 |
20 |
3015.2.ct |
\(\chi_{3015}(76, \cdot)\) |
n/a |
5440 |
20 |
3015.2.cw |
\(\chi_{3015}(62, \cdot)\) |
n/a |
2720 |
20 |
3015.2.cx |
\(\chi_{3015}(253, \cdot)\) |
n/a |
3360 |
20 |
3015.2.cz |
\(\chi_{3015}(41, \cdot)\) |
n/a |
5440 |
20 |
3015.2.db |
\(\chi_{3015}(74, \cdot)\) |
n/a |
8080 |
20 |
3015.2.df |
\(\chi_{3015}(19, \cdot)\) |
n/a |
3360 |
20 |
3015.2.dg |
\(\chi_{3015}(349, \cdot)\) |
n/a |
8080 |
20 |
3015.2.dj |
\(\chi_{3015}(119, \cdot)\) |
n/a |
8080 |
20 |
3015.2.dk |
\(\chi_{3015}(44, \cdot)\) |
n/a |
2720 |
20 |
3015.2.dl |
\(\chi_{3015}(49, \cdot)\) |
n/a |
8080 |
20 |
3015.2.dq |
\(\chi_{3015}(176, \cdot)\) |
n/a |
5440 |
20 |
3015.2.dr |
\(\chi_{3015}(251, \cdot)\) |
n/a |
1840 |
20 |
3015.2.du |
\(\chi_{3015}(11, \cdot)\) |
n/a |
5440 |
20 |
3015.2.dx |
\(\chi_{3015}(4, \cdot)\) |
n/a |
8080 |
20 |
3015.2.dz |
\(\chi_{3015}(599, \cdot)\) |
n/a |
8080 |
20 |
3015.2.ec |
\(\chi_{3015}(17, \cdot)\) |
n/a |
5440 |
40 |
3015.2.ed |
\(\chi_{3015}(43, \cdot)\) |
n/a |
16160 |
40 |
3015.2.ee |
\(\chi_{3015}(92, \cdot)\) |
n/a |
16160 |
40 |
3015.2.ef |
\(\chi_{3015}(28, \cdot)\) |
n/a |
6720 |
40 |
3015.2.ek |
\(\chi_{3015}(7, \cdot)\) |
n/a |
16160 |
40 |
3015.2.el |
\(\chi_{3015}(23, \cdot)\) |
n/a |
16160 |
40 |
3015.2.em |
\(\chi_{3015}(178, \cdot)\) |
n/a |
16160 |
40 |
3015.2.en |
\(\chi_{3015}(83, \cdot)\) |
n/a |
16160 |
40 |
"n/a" means that newforms for that character have not been added to the database yet