Defining parameters
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(20\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(35, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 12 | 6 |
Cusp forms | 14 | 12 | 2 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(35, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
35.5.d.a | $12$ | $3.618$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-6\) | \(0\) | \(0\) | \(-50\) | \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(35, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)