Defining parameters
Level: | \( N \) | = | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(7680\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(112))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3540 | 1885 | 1655 |
Cusp forms | 3372 | 1841 | 1531 |
Eisenstein series | 168 | 44 | 124 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(112))\)
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 |
---|---|---|---|---|
112.10.a | \(\chi_{112}(1, \cdot)\) | 112.10.a.a | 1 | 1 |
112.10.a.b | 1 | |||
112.10.a.c | 2 | |||
112.10.a.d | 2 | |||
112.10.a.e | 2 | |||
112.10.a.f | 2 | |||
112.10.a.g | 3 | |||
112.10.a.h | 3 | |||
112.10.a.i | 3 | |||
112.10.a.j | 4 | |||
112.10.a.k | 4 | |||
112.10.b | \(\chi_{112}(57, \cdot)\) | None | 0 | 1 |
112.10.e | \(\chi_{112}(55, \cdot)\) | None | 0 | 1 |
112.10.f | \(\chi_{112}(111, \cdot)\) | 112.10.f.a | 12 | 1 |
112.10.f.b | 24 | |||
112.10.i | \(\chi_{112}(65, \cdot)\) | 112.10.i.a | 6 | 2 |
112.10.i.b | 6 | |||
112.10.i.c | 10 | |||
112.10.i.d | 12 | |||
112.10.i.e | 18 | |||
112.10.i.f | 18 | |||
112.10.j | \(\chi_{112}(27, \cdot)\) | n/a | 284 | 2 |
112.10.m | \(\chi_{112}(29, \cdot)\) | n/a | 216 | 2 |
112.10.p | \(\chi_{112}(31, \cdot)\) | 112.10.p.a | 24 | 2 |
112.10.p.b | 24 | |||
112.10.p.c | 24 | |||
112.10.q | \(\chi_{112}(87, \cdot)\) | None | 0 | 2 |
112.10.t | \(\chi_{112}(9, \cdot)\) | None | 0 | 2 |
112.10.v | \(\chi_{112}(3, \cdot)\) | n/a | 568 | 4 |
112.10.w | \(\chi_{112}(37, \cdot)\) | n/a | 568 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)