Defining parameters
Level: | \( N \) | = | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(51840\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(342))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22968 | 5953 | 17015 |
Cusp forms | 22392 | 5953 | 16439 |
Eisenstein series | 576 | 0 | 576 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(342))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)