Defining parameters
Level: | \( N \) | = | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(42))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 312 | 68 | 244 |
Cusp forms | 264 | 68 | 196 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(42))\)
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 \(S_{7}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)