Defining parameters
Level: | \( N \) | = | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 14 \) |
Nonzero newspaces: | \( 6 \) | ||
Sturm bound: | \(5600\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(75))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2656 | 1817 | 839 |
Cusp forms | 2544 | 1777 | 767 |
Eisenstein series | 112 | 40 | 72 |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(75))\)
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 |
---|---|---|---|---|
75.14.a | \(\chi_{75}(1, \cdot)\) | 75.14.a.a | 1 | 1 |
75.14.a.b | 1 | |||
75.14.a.c | 2 | |||
75.14.a.d | 2 | |||
75.14.a.e | 2 | |||
75.14.a.f | 3 | |||
75.14.a.g | 4 | |||
75.14.a.h | 4 | |||
75.14.a.i | 5 | |||
75.14.a.j | 5 | |||
75.14.a.k | 6 | |||
75.14.a.l | 6 | |||
75.14.b | \(\chi_{75}(49, \cdot)\) | 75.14.b.a | 2 | 1 |
75.14.b.b | 2 | |||
75.14.b.c | 4 | |||
75.14.b.d | 4 | |||
75.14.b.e | 4 | |||
75.14.b.f | 6 | |||
75.14.b.g | 8 | |||
75.14.b.h | 10 | |||
75.14.e | \(\chi_{75}(32, \cdot)\) | n/a | 152 | 2 |
75.14.g | \(\chi_{75}(16, \cdot)\) | n/a | 264 | 4 |
75.14.i | \(\chi_{75}(4, \cdot)\) | n/a | 256 | 4 |
75.14.l | \(\chi_{75}(2, \cdot)\) | n/a | 1024 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)