Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8047))\).
|
Total |
New |
Old |
Modular forms
| 2689536 |
2656963 |
32573 |
Cusp forms
| 2674705 |
2643387 |
31318 |
Eisenstein series
| 14831 |
13576 |
1255 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8047))\)
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 |
8047.2.a |
\(\chi_{8047}(1, \cdot)\) |
8047.2.a.a |
2 |
1 |
8047.2.a.b |
142 |
8047.2.a.c |
151 |
8047.2.a.d |
156 |
8047.2.a.e |
168 |
8047.2.c |
\(\chi_{8047}(1858, \cdot)\) |
n/a |
720 |
1 |
8047.2.e |
\(\chi_{8047}(3461, \cdot)\) |
n/a |
1442 |
2 |
8047.2.f |
\(\chi_{8047}(620, \cdot)\) |
n/a |
1444 |
2 |
8047.2.g |
\(\chi_{8047}(3966, \cdot)\) |
n/a |
1240 |
2 |
8047.2.h |
\(\chi_{8047}(2109, \cdot)\) |
n/a |
1442 |
2 |
8047.2.i |
\(\chi_{8047}(2475, \cdot)\) |
n/a |
1440 |
2 |
8047.2.k |
\(\chi_{8047}(6556, \cdot)\) |
n/a |
1442 |
2 |
8047.2.q |
\(\chi_{8047}(1239, \cdot)\) |
n/a |
1440 |
2 |
8047.2.r |
\(\chi_{8047}(985, \cdot)\) |
n/a |
1442 |
2 |
8047.2.u |
\(\chi_{8047}(5823, \cdot)\) |
n/a |
1444 |
2 |
8047.2.w |
\(\chi_{8047}(5205, \cdot)\) |
n/a |
2888 |
4 |
8047.2.ba |
\(\chi_{8047}(253, \cdot)\) |
n/a |
2884 |
4 |
8047.2.bb |
\(\chi_{8047}(618, \cdot)\) |
n/a |
2888 |
4 |
8047.2.bc |
\(\chi_{8047}(1605, \cdot)\) |
n/a |
2884 |
4 |
8047.2.be |
\(\chi_{8047}(79, \cdot)\) |
n/a |
63240 |
102 |
8047.2.bg |
\(\chi_{8047}(38, \cdot)\) |
n/a |
73440 |
102 |
8047.2.bi |
\(\chi_{8047}(16, \cdot)\) |
n/a |
147084 |
204 |
8047.2.bj |
\(\chi_{8047}(53, \cdot)\) |
n/a |
126480 |
204 |
8047.2.bk |
\(\chi_{8047}(9, \cdot)\) |
n/a |
147288 |
204 |
8047.2.bl |
\(\chi_{8047}(61, \cdot)\) |
n/a |
147084 |
204 |
8047.2.bn |
\(\chi_{8047}(8, \cdot)\) |
n/a |
146880 |
204 |
8047.2.bp |
\(\chi_{8047}(25, \cdot)\) |
n/a |
147288 |
204 |
8047.2.bs |
\(\chi_{8047}(36, \cdot)\) |
n/a |
147084 |
204 |
8047.2.bt |
\(\chi_{8047}(127, \cdot)\) |
n/a |
147288 |
204 |
8047.2.bz |
\(\chi_{8047}(4, \cdot)\) |
n/a |
147084 |
204 |
8047.2.cb |
\(\chi_{8047}(59, \cdot)\) |
n/a |
294168 |
408 |
8047.2.cc |
\(\chi_{8047}(50, \cdot)\) |
n/a |
294576 |
408 |
8047.2.cd |
\(\chi_{8047}(2, \cdot)\) |
n/a |
294168 |
408 |
8047.2.ch |
\(\chi_{8047}(18, \cdot)\) |
n/a |
294576 |
408 |
"n/a" means that newforms for that character have not been added to the database yet