Defining parameters
Level: | \( N \) | = | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 50 \) | ||
Sturm bound: | \(145152\) | ||
Trace bound: | \(10\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(585))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 61248 | 43664 | 17584 |
Cusp forms | 59712 | 43068 | 16644 |
Eisenstein series | 1536 | 596 | 940 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(585))\)
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 \(S_{6}^{\mathrm{old}}(\Gamma_1(585))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(585)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 1}\)