Defining parameters
Level: | \( N \) | = | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 14 \) | ||
Newform subspaces: | \( 31 \) | ||
Sturm bound: | \(9216\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(240))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3296 | 1214 | 2082 |
Cusp forms | 2848 | 1162 | 1686 |
Eisenstein series | 448 | 52 | 396 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(240))\)
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.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)