Defining parameters
Level: | \( N \) | = | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(17280\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(176))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7820 | 4289 | 3531 |
Cusp forms | 7540 | 4207 | 3333 |
Eisenstein series | 280 | 82 | 198 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(176))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
176.9.b | \(\chi_{176}(153, \cdot)\) | None | 0 | 1 |
176.9.d | \(\chi_{176}(111, \cdot)\) | 176.9.d.a | 12 | 1 |
176.9.d.b | 28 | |||
176.9.f | \(\chi_{176}(23, \cdot)\) | None | 0 | 1 |
176.9.h | \(\chi_{176}(65, \cdot)\) | 176.9.h.a | 1 | 1 |
176.9.h.b | 2 | |||
176.9.h.c | 6 | |||
176.9.h.d | 6 | |||
176.9.h.e | 8 | |||
176.9.h.f | 24 | |||
176.9.k | \(\chi_{176}(67, \cdot)\) | n/a | 320 | 2 |
176.9.l | \(\chi_{176}(21, \cdot)\) | n/a | 380 | 2 |
176.9.n | \(\chi_{176}(17, \cdot)\) | n/a | 188 | 4 |
176.9.p | \(\chi_{176}(71, \cdot)\) | None | 0 | 4 |
176.9.r | \(\chi_{176}(15, \cdot)\) | n/a | 192 | 4 |
176.9.t | \(\chi_{176}(41, \cdot)\) | None | 0 | 4 |
176.9.u | \(\chi_{176}(13, \cdot)\) | n/a | 1520 | 8 |
176.9.v | \(\chi_{176}(3, \cdot)\) | n/a | 1520 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(176)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)