Defining parameters
Level: | \( N \) | = | \( 1156 = 2^{2} \cdot 17^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(166464\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1156))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42616 | 24476 | 18140 |
Cusp forms | 40617 | 23740 | 16877 |
Eisenstein series | 1999 | 736 | 1263 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)
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 |
---|---|---|---|---|
1156.2.a | \(\chi_{1156}(1, \cdot)\) | 1156.2.a.a | 2 | 1 |
1156.2.a.b | 2 | |||
1156.2.a.c | 2 | |||
1156.2.a.d | 2 | |||
1156.2.a.e | 3 | |||
1156.2.a.f | 3 | |||
1156.2.a.g | 4 | |||
1156.2.a.h | 4 | |||
1156.2.b | \(\chi_{1156}(577, \cdot)\) | 1156.2.b.a | 4 | 1 |
1156.2.b.b | 4 | |||
1156.2.b.c | 4 | |||
1156.2.b.d | 4 | |||
1156.2.b.e | 6 | |||
1156.2.e | \(\chi_{1156}(829, \cdot)\) | 1156.2.e.a | 2 | 2 |
1156.2.e.b | 2 | |||
1156.2.e.c | 4 | |||
1156.2.e.d | 8 | |||
1156.2.e.e | 8 | |||
1156.2.e.f | 8 | |||
1156.2.e.g | 12 | |||
1156.2.h | \(\chi_{1156}(733, \cdot)\) | 1156.2.h.a | 4 | 4 |
1156.2.h.b | 4 | |||
1156.2.h.c | 4 | |||
1156.2.h.d | 8 | |||
1156.2.h.e | 16 | |||
1156.2.h.f | 16 | |||
1156.2.h.g | 16 | |||
1156.2.h.h | 24 | |||
1156.2.i | \(\chi_{1156}(75, \cdot)\) | n/a | 968 | 8 |
1156.2.k | \(\chi_{1156}(69, \cdot)\) | n/a | 416 | 16 |
1156.2.n | \(\chi_{1156}(33, \cdot)\) | n/a | 416 | 16 |
1156.2.p | \(\chi_{1156}(13, \cdot)\) | n/a | 832 | 32 |
1156.2.q | \(\chi_{1156}(9, \cdot)\) | n/a | 1600 | 64 |
1156.2.t | \(\chi_{1156}(3, \cdot)\) | n/a | 19328 | 128 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1156))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1156)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)