Defining parameters
Level: | \( N \) | = | \( 30 = 2 \cdot 3 \cdot 5 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(30))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 16 | 72 |
Cusp forms | 56 | 16 | 40 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)
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 |
---|---|---|---|---|
30.4.a | \(\chi_{30}(1, \cdot)\) | 30.4.a.a | 1 | 1 |
30.4.a.b | 1 | |||
30.4.c | \(\chi_{30}(19, \cdot)\) | 30.4.c.a | 2 | 1 |
30.4.e | \(\chi_{30}(17, \cdot)\) | 30.4.e.a | 12 | 2 |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(30)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 1}\)