Defining parameters
| Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 60.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(48\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(60, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 42 | 2 | 40 |
| Cusp forms | 30 | 2 | 28 |
| Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(60, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 60.4.d.a | $2$ | $3.540$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-20\) | \(0\) | \(q+3 i q^{3}+(5 i-10)q^{5}+22 i q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(60, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(60, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)