Defining parameters
Level: | \( N \) | = | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | = | \( 5 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(12000\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(175))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4968 | 4343 | 625 |
Cusp forms | 4632 | 4137 | 495 |
Eisenstein series | 336 | 206 | 130 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(175))\)
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 |
---|---|---|---|---|
175.5.c | \(\chi_{175}(174, \cdot)\) | 175.5.c.a | 2 | 1 |
175.5.c.b | 4 | |||
175.5.c.c | 16 | |||
175.5.c.d | 24 | |||
175.5.d | \(\chi_{175}(76, \cdot)\) | 175.5.d.a | 1 | 1 |
175.5.d.b | 2 | |||
175.5.d.c | 2 | |||
175.5.d.d | 2 | |||
175.5.d.e | 4 | |||
175.5.d.f | 8 | |||
175.5.d.g | 8 | |||
175.5.d.h | 8 | |||
175.5.d.i | 12 | |||
175.5.g | \(\chi_{175}(43, \cdot)\) | 175.5.g.a | 4 | 2 |
175.5.g.b | 12 | |||
175.5.g.c | 24 | |||
175.5.g.d | 32 | |||
175.5.i | \(\chi_{175}(26, \cdot)\) | 175.5.i.a | 4 | 2 |
175.5.i.b | 20 | |||
175.5.i.c | 22 | |||
175.5.i.d | 22 | |||
175.5.i.e | 28 | |||
175.5.j | \(\chi_{175}(24, \cdot)\) | 175.5.j.a | 8 | 2 |
175.5.j.b | 40 | |||
175.5.j.c | 44 | |||
175.5.l | \(\chi_{175}(6, \cdot)\) | n/a | 312 | 4 |
175.5.m | \(\chi_{175}(34, \cdot)\) | n/a | 312 | 4 |
175.5.p | \(\chi_{175}(18, \cdot)\) | n/a | 184 | 4 |
175.5.r | \(\chi_{175}(8, \cdot)\) | n/a | 480 | 8 |
175.5.u | \(\chi_{175}(19, \cdot)\) | n/a | 624 | 8 |
175.5.v | \(\chi_{175}(31, \cdot)\) | n/a | 624 | 8 |
175.5.w | \(\chi_{175}(2, \cdot)\) | n/a | 1248 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces
\( S_{5}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)