Defining parameters
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(72, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 31 | 45 |
Cusp forms | 68 | 29 | 39 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(72, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
72.7.b.a | $1$ | $16.564$ | \(\Q\) | \(\Q(\sqrt{-2}) \) | \(8\) | \(0\) | \(0\) | \(0\) | \(q+8q^{2}+2^{6}q^{4}+2^{9}q^{8}+2338q^{11}+\cdots\) |
72.7.b.b | $4$ | $16.564$ | 4.0.3803625.2 | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-11+\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\) |
72.7.b.c | $12$ | $16.564$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-10\) | \(0\) | \(0\) | \(0\) | \(q+(-1-\beta _{1})q^{2}+(2+\beta _{1}+\beta _{5})q^{4}+\cdots\) |
72.7.b.d | $12$ | $16.564$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-13+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(72, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)