Defining parameters
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(144, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 12 | 144 |
Cusp forms | 132 | 12 | 120 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(144, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
144.7.e.a | $2$ | $33.128$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(-1048\) | \(q+5\beta q^{5}-524q^{7}+68\beta q^{11}+344q^{13}+\cdots\) |
144.7.e.b | $2$ | $33.128$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(-120\) | \(q+5\beta q^{5}-60q^{7}-236\beta q^{11}+1192q^{13}+\cdots\) |
144.7.e.c | $2$ | $33.128$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(488\) | \(q+5\beta q^{5}+244q^{7}-188\beta q^{11}-2728q^{13}+\cdots\) |
144.7.e.d | $2$ | $33.128$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(968\) | \(q+41\beta q^{5}+22^{2}q^{7}-316\beta q^{11}+3368q^{13}+\cdots\) |
144.7.e.e | $4$ | $33.128$ | \(\Q(\sqrt{-2}, \sqrt{145})\) | None | \(0\) | \(0\) | \(0\) | \(432\) | \(q+(-5^{2}\beta _{1}-\beta _{3})q^{5}+(108+\beta _{2})q^{7}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(144, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)