Defining parameters
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.k (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(75, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 656 | 320 | 336 |
Cusp forms | 624 | 320 | 304 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(75, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
75.9.k.a | $320$ | $30.553$ | None | \(0\) | \(0\) | \(444\) | \(-4540\) |
Decomposition of \(S_{9}^{\mathrm{old}}(75, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)