Defining parameters
Level: | \( N \) | = | \( 306 = 2 \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 10 \) | ||
Newform subspaces: | \( 47 \) | ||
Sturm bound: | \(10368\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(306))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2848 | 680 | 2168 |
Cusp forms | 2337 | 680 | 1657 |
Eisenstein series | 511 | 0 | 511 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)
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.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(306))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(306)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)