Defining parameters
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.s (of order \(16\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
Character field: | \(\Q(\zeta_{16})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(136, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 448 | 448 | 0 |
Cusp forms | 416 | 416 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(136, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
136.4.s.a | $8$ | $8.024$ | \(\Q(\zeta_{16})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(-8\) | \(0\) | \(0\) | \(q+(2\zeta_{16}-2\zeta_{16}^{5})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\) |
136.4.s.b | $8$ | $8.024$ | \(\Q(\zeta_{16})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(8\) | \(0\) | \(0\) | \(q+(-2\zeta_{16}+2\zeta_{16}^{5})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\) |
136.4.s.c | $400$ | $8.024$ | None | \(-8\) | \(-16\) | \(0\) | \(0\) |