Defining parameters
Level: | \( N \) | = | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 6 \) | ||
Sturm bound: | \(8400\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(150))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3712 | 830 | 2882 |
Cusp forms | 3488 | 830 | 2658 |
Eisenstein series | 224 | 0 | 224 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(150))\)
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 |
---|---|---|---|---|
150.7.b | \(\chi_{150}(149, \cdot)\) | 150.7.b.a | 4 | 1 |
150.7.b.b | 16 | |||
150.7.b.c | 16 | |||
150.7.d | \(\chi_{150}(101, \cdot)\) | 150.7.d.a | 2 | 1 |
150.7.d.b | 8 | |||
150.7.d.c | 8 | |||
150.7.d.d | 8 | |||
150.7.d.e | 12 | |||
150.7.f | \(\chi_{150}(7, \cdot)\) | 150.7.f.a | 4 | 2 |
150.7.f.b | 4 | |||
150.7.f.c | 4 | |||
150.7.f.d | 4 | |||
150.7.f.e | 4 | |||
150.7.f.f | 4 | |||
150.7.f.g | 4 | |||
150.7.f.h | 8 | |||
150.7.i | \(\chi_{150}(29, \cdot)\) | n/a | 240 | 4 |
150.7.j | \(\chi_{150}(11, \cdot)\) | n/a | 240 | 4 |
150.7.k | \(\chi_{150}(13, \cdot)\) | n/a | 240 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)