Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(19\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(10, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 12 | 28 |
Cusp forms | 32 | 12 | 20 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(10, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
10.13.c.a | $6$ | $9.140$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(-192\) | \(-936\) | \(-16260\) | \(-45336\) | \(q+(-2^{5}-2^{5}\beta _{1})q^{2}+(-156+156\beta _{1}+\cdots)q^{3}+\cdots\) |
10.13.c.b | $6$ | $9.140$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(192\) | \(296\) | \(14460\) | \(-322104\) | \(q+(2^{5}+2^{5}\beta _{1})q^{2}+(7^{2}-7^{2}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{13}^{\mathrm{old}}(10, [\chi])\) into lower level spaces
\( S_{13}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{13}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)