Defining parameters
| Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 135.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(72\) | ||
| Trace bound: | \(1\) | ||
| Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(135, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 60 | 24 | 36 |
| Cusp forms | 48 | 24 | 24 |
| Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(135, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 135.4.b.a | $4$ | $7.965$ | \(\Q(i, \sqrt{5})\) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-13-\beta _{3})q^{4}-5\beta _{1}q^{5}+\cdots\) |
| 135.4.b.b | $8$ | $7.965$ | 8.0.\(\cdots\).7 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}-2\beta _{5}+\cdots)q^{5}+\cdots\) |
| 135.4.b.c | $12$ | $7.965$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{7}q^{2}+(-5-\beta _{1})q^{4}-\beta _{3}q^{5}+\beta _{8}q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(135, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(135, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)