Defining parameters
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(26, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 14 | 40 |
Cusp forms | 46 | 14 | 32 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(26, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
26.8.c.a | $6$ | $8.122$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(-24\) | \(0\) | \(-666\) | \(1160\) | \(q+(-8-8\beta _{3})q^{2}-\beta _{1}q^{3}+2^{6}\beta _{3}q^{4}+\cdots\) |
26.8.c.b | $8$ | $8.122$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(32\) | \(0\) | \(556\) | \(-548\) | \(q-8\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{6}-2^{6}\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(26, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)