Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1053))\).
|
Total |
New |
Old |
Modular forms
| 42120 |
32488 |
9632 |
Cusp forms
| 39529 |
31256 |
8273 |
Eisenstein series
| 2591 |
1232 |
1359 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)
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 |
1053.2.a |
\(\chi_{1053}(1, \cdot)\) |
1053.2.a.a |
1 |
1 |
1053.2.a.b |
1 |
1053.2.a.c |
1 |
1053.2.a.d |
1 |
1053.2.a.e |
2 |
1053.2.a.f |
2 |
1053.2.a.g |
3 |
1053.2.a.h |
3 |
1053.2.a.i |
4 |
1053.2.a.j |
5 |
1053.2.a.k |
5 |
1053.2.a.l |
6 |
1053.2.a.m |
6 |
1053.2.a.n |
8 |
1053.2.b |
\(\chi_{1053}(649, \cdot)\) |
1053.2.b.a |
2 |
1 |
1053.2.b.b |
2 |
1053.2.b.c |
2 |
1053.2.b.d |
2 |
1053.2.b.e |
2 |
1053.2.b.f |
2 |
1053.2.b.g |
4 |
1053.2.b.h |
4 |
1053.2.b.i |
10 |
1053.2.b.j |
10 |
1053.2.b.k |
12 |
1053.2.e |
\(\chi_{1053}(352, \cdot)\) |
1053.2.e.a |
2 |
2 |
1053.2.e.b |
2 |
1053.2.e.c |
2 |
1053.2.e.d |
2 |
1053.2.e.e |
4 |
1053.2.e.f |
4 |
1053.2.e.g |
4 |
1053.2.e.h |
4 |
1053.2.e.i |
4 |
1053.2.e.j |
4 |
1053.2.e.k |
4 |
1053.2.e.l |
4 |
1053.2.e.m |
4 |
1053.2.e.n |
6 |
1053.2.e.o |
6 |
1053.2.e.p |
8 |
1053.2.e.q |
8 |
1053.2.e.r |
8 |
1053.2.e.s |
16 |
1053.2.f |
\(\chi_{1053}(217, \cdot)\) |
n/a |
108 |
2 |
1053.2.g |
\(\chi_{1053}(406, \cdot)\) |
n/a |
104 |
2 |
1053.2.h |
\(\chi_{1053}(55, \cdot)\) |
n/a |
108 |
2 |
1053.2.i |
\(\chi_{1053}(161, \cdot)\) |
n/a |
104 |
2 |
1053.2.l |
\(\chi_{1053}(433, \cdot)\) |
n/a |
108 |
2 |
1053.2.q |
\(\chi_{1053}(82, \cdot)\) |
n/a |
104 |
2 |
1053.2.r |
\(\chi_{1053}(595, \cdot)\) |
n/a |
108 |
2 |
1053.2.t |
\(\chi_{1053}(298, \cdot)\) |
n/a |
108 |
2 |
1053.2.w |
\(\chi_{1053}(118, \cdot)\) |
n/a |
216 |
6 |
1053.2.x |
\(\chi_{1053}(289, \cdot)\) |
n/a |
240 |
6 |
1053.2.y |
\(\chi_{1053}(100, \cdot)\) |
n/a |
240 |
6 |
1053.2.ba |
\(\chi_{1053}(215, \cdot)\) |
n/a |
216 |
4 |
1053.2.bc |
\(\chi_{1053}(512, \cdot)\) |
n/a |
216 |
4 |
1053.2.bd |
\(\chi_{1053}(80, \cdot)\) |
n/a |
208 |
4 |
1053.2.bf |
\(\chi_{1053}(188, \cdot)\) |
n/a |
216 |
4 |
1053.2.bl |
\(\chi_{1053}(64, \cdot)\) |
n/a |
240 |
6 |
1053.2.bn |
\(\chi_{1053}(127, \cdot)\) |
n/a |
240 |
6 |
1053.2.bo |
\(\chi_{1053}(10, \cdot)\) |
n/a |
240 |
6 |
1053.2.bq |
\(\chi_{1053}(40, \cdot)\) |
n/a |
1944 |
18 |
1053.2.br |
\(\chi_{1053}(16, \cdot)\) |
n/a |
2232 |
18 |
1053.2.bs |
\(\chi_{1053}(61, \cdot)\) |
n/a |
2232 |
18 |
1053.2.bt |
\(\chi_{1053}(206, \cdot)\) |
n/a |
480 |
12 |
1053.2.bw |
\(\chi_{1053}(8, \cdot)\) |
n/a |
480 |
12 |
1053.2.by |
\(\chi_{1053}(71, \cdot)\) |
n/a |
480 |
12 |
1053.2.bz |
\(\chi_{1053}(43, \cdot)\) |
n/a |
2232 |
18 |
1053.2.cd |
\(\chi_{1053}(25, \cdot)\) |
n/a |
2232 |
18 |
1053.2.ce |
\(\chi_{1053}(4, \cdot)\) |
n/a |
2232 |
18 |
1053.2.cl |
\(\chi_{1053}(5, \cdot)\) |
n/a |
4464 |
36 |
1053.2.cm |
\(\chi_{1053}(20, \cdot)\) |
n/a |
4464 |
36 |
1053.2.cn |
\(\chi_{1053}(2, \cdot)\) |
n/a |
4464 |
36 |
"n/a" means that newforms for that character have not been added to the database yet