Defining parameters
| Level: | \( N \) | \(=\) | \( 5160 = 2^{3} \cdot 3 \cdot 5 \cdot 43 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5160.gc (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 172 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2112\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5160, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12864 | 0 | 12864 |
| Cusp forms | 12480 | 0 | 12480 |
| Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{old}}(5160, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(172, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(516, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(860, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2580, [\chi])\)\(^{\oplus 2}\)