Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(847))\).
|
Total |
New |
Old |
Modular forms
| 30000 |
28075 |
1925 |
Cusp forms
| 28081 |
26671 |
1410 |
Eisenstein series
| 1919 |
1404 |
515 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)
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 |
847.2.a |
\(\chi_{847}(1, \cdot)\) |
847.2.a.a |
1 |
1 |
847.2.a.b |
1 |
847.2.a.c |
1 |
847.2.a.d |
2 |
847.2.a.e |
2 |
847.2.a.f |
2 |
847.2.a.g |
2 |
847.2.a.h |
2 |
847.2.a.i |
3 |
847.2.a.j |
3 |
847.2.a.k |
4 |
847.2.a.l |
4 |
847.2.a.m |
6 |
847.2.a.n |
6 |
847.2.a.o |
8 |
847.2.a.p |
8 |
847.2.b |
\(\chi_{847}(846, \cdot)\) |
847.2.b.a |
8 |
1 |
847.2.b.b |
8 |
847.2.b.c |
8 |
847.2.b.d |
8 |
847.2.b.e |
16 |
847.2.b.f |
16 |
847.2.e |
\(\chi_{847}(485, \cdot)\) |
847.2.e.a |
4 |
2 |
847.2.e.b |
4 |
847.2.e.c |
6 |
847.2.e.d |
6 |
847.2.e.e |
12 |
847.2.e.f |
14 |
847.2.e.g |
14 |
847.2.e.h |
20 |
847.2.e.i |
20 |
847.2.e.j |
28 |
847.2.f |
\(\chi_{847}(148, \cdot)\) |
847.2.f.a |
4 |
4 |
847.2.f.b |
4 |
847.2.f.c |
4 |
847.2.f.d |
4 |
847.2.f.e |
4 |
847.2.f.f |
4 |
847.2.f.g |
4 |
847.2.f.h |
4 |
847.2.f.i |
4 |
847.2.f.j |
4 |
847.2.f.k |
4 |
847.2.f.l |
4 |
847.2.f.m |
4 |
847.2.f.n |
4 |
847.2.f.o |
8 |
847.2.f.p |
8 |
847.2.f.q |
8 |
847.2.f.r |
8 |
847.2.f.s |
8 |
847.2.f.t |
12 |
847.2.f.u |
12 |
847.2.f.v |
16 |
847.2.f.w |
16 |
847.2.f.x |
16 |
847.2.f.y |
24 |
847.2.f.z |
24 |
847.2.i |
\(\chi_{847}(241, \cdot)\) |
847.2.i.a |
24 |
2 |
847.2.i.b |
48 |
847.2.i.c |
56 |
847.2.l |
\(\chi_{847}(118, \cdot)\) |
847.2.l.a |
8 |
4 |
847.2.l.b |
8 |
847.2.l.c |
8 |
847.2.l.d |
8 |
847.2.l.e |
16 |
847.2.l.f |
16 |
847.2.l.g |
16 |
847.2.l.h |
16 |
847.2.l.i |
16 |
847.2.l.j |
16 |
847.2.l.k |
32 |
847.2.l.l |
32 |
847.2.l.m |
64 |
847.2.m |
\(\chi_{847}(78, \cdot)\) |
847.2.m.a |
320 |
10 |
847.2.m.b |
340 |
847.2.n |
\(\chi_{847}(9, \cdot)\) |
847.2.n.a |
8 |
8 |
847.2.n.b |
8 |
847.2.n.c |
8 |
847.2.n.d |
24 |
847.2.n.e |
24 |
847.2.n.f |
24 |
847.2.n.g |
24 |
847.2.n.h |
40 |
847.2.n.i |
40 |
847.2.n.j |
40 |
847.2.n.k |
48 |
847.2.n.l |
56 |
847.2.n.m |
56 |
847.2.n.n |
112 |
847.2.p |
\(\chi_{847}(76, \cdot)\) |
847.2.p.a |
20 |
10 |
847.2.p.b |
840 |
847.2.r |
\(\chi_{847}(40, \cdot)\) |
847.2.r.a |
48 |
8 |
847.2.r.b |
48 |
847.2.r.c |
48 |
847.2.r.d |
48 |
847.2.r.e |
96 |
847.2.r.f |
224 |
847.2.u |
\(\chi_{847}(23, \cdot)\) |
847.2.u.a |
1720 |
20 |
847.2.v |
\(\chi_{847}(15, \cdot)\) |
847.2.v.a |
1280 |
40 |
847.2.v.b |
1360 |
847.2.x |
\(\chi_{847}(10, \cdot)\) |
847.2.x.a |
1720 |
20 |
847.2.ba |
\(\chi_{847}(6, \cdot)\) |
847.2.ba.a |
80 |
40 |
847.2.ba.b |
3360 |
847.2.bc |
\(\chi_{847}(4, \cdot)\) |
847.2.bc.a |
6880 |
80 |
847.2.be |
\(\chi_{847}(17, \cdot)\) |
847.2.be.a |
6880 |
80 |