Defining parameters
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(45\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(81, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 18 | 24 |
Cusp forms | 30 | 14 | 16 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(81, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
81.5.b.a | $6$ | $8.373$ | 6.0.39400128.1 | None | \(0\) | \(0\) | \(0\) | \(-24\) | \(q+\beta _{1}q^{2}+(-5+\beta _{2})q^{4}+\beta _{4}q^{5}+(-4+\cdots)q^{7}+\cdots\) |
81.5.b.b | $8$ | $8.373$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(52\) | \(q-\beta _{1}q^{2}+(-8+\beta _{5})q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(81, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)