Defining parameters
Level: | \( N \) | = | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 22 \) | ||
Sturm bound: | \(69984\) | ||
Trace bound: | \(21\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(567))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23976 | 17944 | 6032 |
Cusp forms | 22680 | 17384 | 5296 |
Eisenstein series | 1296 | 560 | 736 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(567))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(567))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(567)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)