Defining parameters
Level: | \( N \) | = | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(5376\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(112))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2388 | 1265 | 1123 |
Cusp forms | 2220 | 1219 | 1001 |
Eisenstein series | 168 | 46 | 122 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(112))\)
We only show spaces with odd 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 |
---|---|---|---|---|
112.7.c | \(\chi_{112}(97, \cdot)\) | 112.7.c.a | 1 | 1 |
112.7.c.b | 2 | |||
112.7.c.c | 4 | |||
112.7.c.d | 4 | |||
112.7.c.e | 12 | |||
112.7.d | \(\chi_{112}(15, \cdot)\) | 112.7.d.a | 6 | 1 |
112.7.d.b | 12 | |||
112.7.g | \(\chi_{112}(71, \cdot)\) | None | 0 | 1 |
112.7.h | \(\chi_{112}(41, \cdot)\) | None | 0 | 1 |
112.7.k | \(\chi_{112}(43, \cdot)\) | n/a | 144 | 2 |
112.7.l | \(\chi_{112}(13, \cdot)\) | n/a | 188 | 2 |
112.7.n | \(\chi_{112}(73, \cdot)\) | None | 0 | 2 |
112.7.o | \(\chi_{112}(23, \cdot)\) | None | 0 | 2 |
112.7.r | \(\chi_{112}(79, \cdot)\) | 112.7.r.a | 16 | 2 |
112.7.r.b | 16 | |||
112.7.r.c | 16 | |||
112.7.s | \(\chi_{112}(17, \cdot)\) | 112.7.s.a | 2 | 2 |
112.7.s.b | 4 | |||
112.7.s.c | 8 | |||
112.7.s.d | 8 | |||
112.7.s.e | 24 | |||
112.7.u | \(\chi_{112}(11, \cdot)\) | n/a | 376 | 4 |
112.7.x | \(\chi_{112}(5, \cdot)\) | n/a | 376 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)