Defining parameters
Level: | \( N \) | = | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 40 \) | ||
Sturm bound: | \(138240\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(693))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 52800 | 39082 | 13718 |
Cusp forms | 50880 | 38270 | 12610 |
Eisenstein series | 1920 | 812 | 1108 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(693))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(693))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(693)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 1}\)