Defining parameters
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(26\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(14, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 52 | 16 | 36 |
Cusp forms | 44 | 16 | 28 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(14, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
14.13.d.a | $16$ | $12.796$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(18144\) | \(-469720\) | \(q+(-\beta _{2}-\beta _{4})q^{2}+(5\beta _{2}+2\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{13}^{\mathrm{old}}(14, [\chi])\) into lower level spaces
\( S_{13}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{13}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)