Defining parameters
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.t (of order \(16\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(\zeta_{16})\) | ||
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 | 320 | 72 | 248 |
Cusp forms | 256 | 72 | 184 |
Eisenstein series | 64 | 0 | 64 |
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.t.a | $32$ | $3.706$ | None | \(0\) | \(-8\) | \(0\) | \(8\) | ||
136.3.t.b | $40$ | $3.706$ | None | \(0\) | \(8\) | \(0\) | \(-8\) |
Decomposition of \(S_{3}^{\mathrm{old}}(136, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)