Defining parameters
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(144, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 300 | 72 | 228 |
Cusp forms | 276 | 72 | 204 |
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.o.a | $24$ | $33.128$ | None | \(0\) | \(-48\) | \(-72\) | \(360\) | ||
144.7.o.b | $24$ | $33.128$ | None | \(0\) | \(0\) | \(144\) | \(0\) | ||
144.7.o.c | $24$ | $33.128$ | None | \(0\) | \(48\) | \(-72\) | \(-360\) |
Decomposition of \(S_{7}^{\mathrm{old}}(144, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)