Defining parameters
Level: | \( N \) | \(=\) | \( 656 = 2^{4} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 656.bs (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 41 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(656, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 720 | 176 | 544 |
Cusp forms | 624 | 160 | 464 |
Eisenstein series | 96 | 16 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(656, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
656.2.bs.a | $8$ | $5.238$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+(\zeta_{20}-\zeta_{20}^{3}+\zeta_{20}^{5}-\zeta_{20}^{6}-\zeta_{20}^{7})q^{3}+\cdots\) |
656.2.bs.b | $16$ | $5.238$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(1-\beta _{4}-\beta _{6}+\beta _{9}-\beta _{12}+\beta _{15})q^{3}+\cdots\) |
656.2.bs.c | $24$ | $5.238$ | None | \(0\) | \(2\) | \(0\) | \(0\) | ||
656.2.bs.d | $24$ | $5.238$ | None | \(0\) | \(6\) | \(-10\) | \(8\) | ||
656.2.bs.e | $40$ | $5.238$ | None | \(0\) | \(0\) | \(0\) | \(4\) | ||
656.2.bs.f | $48$ | $5.238$ | None | \(0\) | \(-2\) | \(0\) | \(-4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(656, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)