Defining parameters
Level: | \( N \) | = | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(340704\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(845))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 142872 | 129207 | 13665 |
Cusp forms | 141048 | 127981 | 13067 |
Eisenstein series | 1824 | 1226 | 598 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(845))\)
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 \(S_{6}^{\mathrm{old}}(\Gamma_1(845))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(845)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 1}\)