Defining parameters
Level: | \( N \) | = | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(60))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 616 | 244 | 372 |
Cusp forms | 536 | 228 | 308 |
Eisenstein series | 80 | 16 | 64 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(60))\)
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 the newforms together with their dimension.
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(60)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)