Defining parameters
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(36, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 6 | 36 |
Cusp forms | 30 | 6 | 24 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(36, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
36.4.e.a | $6$ | $2.124$ | 6.0.6831243.2 | None | \(0\) | \(-3\) | \(6\) | \(-6\) | \(q+(-1-\beta _{2})q^{3}+(1-3\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(36, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)