Defining parameters
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
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: | \(36\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(36, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 10 | 56 |
Cusp forms | 54 | 10 | 44 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(36, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
36.6.e.a | $10$ | $5.774$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(12\) | \(-21\) | \(29\) | \(q+(2+2\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(4\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(36, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)