Defining parameters
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.h (of order \(22\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{22})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(115, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 500 | 320 | 180 |
Cusp forms | 460 | 320 | 140 |
Eisenstein series | 40 | 0 | 40 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(115, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
115.5.h.a | $320$ | $11.888$ | None | \(-12\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{5}^{\mathrm{old}}(115, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)