Defining parameters
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
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: | \(63\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(81, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 26 | 34 |
Cusp forms | 48 | 22 | 26 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(81, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
81.7.b.a | $10$ | $18.634$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(242\) | \(q-\beta _{1}q^{2}+(-5^{2}-\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\) |
81.7.b.b | $12$ | $18.634$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-480\) | \(q-\beta _{2}q^{2}+(-2^{5}+\beta _{1})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(81, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)