Defining parameters
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.n (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(136, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 20 | 68 |
Cusp forms | 56 | 20 | 36 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(136, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
136.2.n.a | $4$ | $1.086$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(4\) | \(-4\) | \(q+(-1-\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\) |
136.2.n.b | $4$ | $1.086$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(-8\) | \(4\) | \(q+(1+\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}+\cdots)q^{5}+\cdots\) |
136.2.n.c | $12$ | $1.086$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+\beta _{2}q^{3}+\beta _{8}q^{5}+(1-\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(136, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)