Defining parameters
Level: | \( N \) | = | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(348480\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(847))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 146160 | 137561 | 8599 |
Cusp forms | 144240 | 136157 | 8083 |
Eisenstein series | 1920 | 1404 | 516 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(847))\)
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 \(S_{6}^{\mathrm{old}}(\Gamma_1(847))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(847)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)