Defining parameters
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(136, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 76 | 0 |
Cusp forms | 68 | 68 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(136, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
136.3.j.a | $4$ | $3.706$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(4\) | \(0\) | \(0\) | \(q+2\zeta_{8}^{2}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}-4q^{4}+\cdots\) |
136.3.j.b | $64$ | $3.706$ | None | \(0\) | \(-8\) | \(0\) | \(0\) |