Defining parameters
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(72, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 6 | 74 |
Cusp forms | 64 | 6 | 58 |
Eisenstein series | 16 | 0 | 16 |
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.e.a | $2$ | $16.564$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(120\) | \(q+5\beta q^{5}+60q^{7}+236\beta q^{11}+1192q^{13}+\cdots\) |
72.7.e.b | $4$ | $16.564$ | \(\Q(\sqrt{-2}, \sqrt{145})\) | None | \(0\) | \(0\) | \(0\) | \(-432\) | \(q+(-5^{2}\beta _{1}-\beta _{3})q^{5}+(-108-\beta _{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(72, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)