Defining parameters
Level: | \( N \) | = | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 30 \) | ||
Sturm bound: | \(43008\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(273))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 19104 | 13468 | 5636 |
Cusp forms | 18528 | 13252 | 5276 |
Eisenstein series | 576 | 216 | 360 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(273))\)
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 the newforms together with their dimension.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(273))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(273)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)