Defining parameters
Level: | \( N \) | = | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(3600\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(75))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1656 | 1128 | 528 |
Cusp forms | 1544 | 1086 | 458 |
Eisenstein series | 112 | 42 | 70 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(75))\)
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 |
---|---|---|---|---|
75.9.c | \(\chi_{75}(26, \cdot)\) | 75.9.c.a | 1 | 1 |
75.9.c.b | 1 | |||
75.9.c.c | 2 | |||
75.9.c.d | 2 | |||
75.9.c.e | 10 | |||
75.9.c.f | 10 | |||
75.9.c.g | 10 | |||
75.9.c.h | 12 | |||
75.9.d | \(\chi_{75}(74, \cdot)\) | 75.9.d.a | 2 | 1 |
75.9.d.b | 4 | |||
75.9.d.c | 20 | |||
75.9.d.d | 20 | |||
75.9.f | \(\chi_{75}(7, \cdot)\) | 75.9.f.a | 4 | 2 |
75.9.f.b | 8 | |||
75.9.f.c | 8 | |||
75.9.f.d | 12 | |||
75.9.f.e | 16 | |||
75.9.h | \(\chi_{75}(14, \cdot)\) | 75.9.h.a | 312 | 4 |
75.9.j | \(\chi_{75}(11, \cdot)\) | 75.9.j.a | 312 | 4 |
75.9.k | \(\chi_{75}(13, \cdot)\) | 75.9.k.a | 320 | 8 |
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)