Defining parameters
Level: | \( N \) | = | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(24000\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(175))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10968 | 9641 | 1327 |
Cusp forms | 10632 | 9437 | 1195 |
Eisenstein series | 336 | 204 | 132 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(175))\)
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 |
---|---|---|---|---|
175.10.a | \(\chi_{175}(1, \cdot)\) | 175.10.a.a | 1 | 1 |
175.10.a.b | 2 | |||
175.10.a.c | 2 | |||
175.10.a.d | 3 | |||
175.10.a.e | 4 | |||
175.10.a.f | 5 | |||
175.10.a.g | 6 | |||
175.10.a.h | 8 | |||
175.10.a.i | 8 | |||
175.10.a.j | 10 | |||
175.10.a.k | 10 | |||
175.10.a.l | 13 | |||
175.10.a.m | 13 | |||
175.10.b | \(\chi_{175}(99, \cdot)\) | 175.10.b.a | 2 | 1 |
175.10.b.b | 4 | |||
175.10.b.c | 4 | |||
175.10.b.d | 6 | |||
175.10.b.e | 8 | |||
175.10.b.f | 10 | |||
175.10.b.g | 12 | |||
175.10.b.h | 16 | |||
175.10.b.i | 20 | |||
175.10.e | \(\chi_{175}(51, \cdot)\) | n/a | 222 | 2 |
175.10.f | \(\chi_{175}(118, \cdot)\) | n/a | 212 | 2 |
175.10.h | \(\chi_{175}(36, \cdot)\) | n/a | 544 | 4 |
175.10.k | \(\chi_{175}(74, \cdot)\) | n/a | 212 | 2 |
175.10.n | \(\chi_{175}(29, \cdot)\) | n/a | 536 | 4 |
175.10.o | \(\chi_{175}(68, \cdot)\) | n/a | 424 | 4 |
175.10.q | \(\chi_{175}(11, \cdot)\) | n/a | 1424 | 8 |
175.10.s | \(\chi_{175}(13, \cdot)\) | n/a | 1424 | 8 |
175.10.t | \(\chi_{175}(4, \cdot)\) | n/a | 1424 | 8 |
175.10.x | \(\chi_{175}(3, \cdot)\) | n/a | 2848 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)