Defining parameters
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(72, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 86 | 122 |
Cusp forms | 200 | 84 | 116 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(72, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
72.18.d.a | $2$ | $131.920$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(18376324\) | \(q-2^{7}\beta q^{2}-2^{17}q^{4}+493679\beta q^{5}+\cdots\) |
72.18.d.b | $16$ | $131.920$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-270\) | \(0\) | \(0\) | \(11529600\) | \(q+(-17-\beta _{1})q^{2}+(-1713+17\beta _{1}+\cdots)q^{4}+\cdots\) |
72.18.d.c | $32$ | $131.920$ | None | \(0\) | \(0\) | \(0\) | \(4682880\) | ||
72.18.d.d | $34$ | $131.920$ | None | \(542\) | \(0\) | \(0\) | \(-23059204\) |
Decomposition of \(S_{18}^{\mathrm{old}}(72, [\chi])\) into lower level spaces
\( S_{18}^{\mathrm{old}}(72, [\chi]) \cong \)