Defining parameters
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(144, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 200 | 82 | 118 |
Cusp forms | 184 | 78 | 106 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(144, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
144.5.m.a | $14$ | $14.885$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(2\) | \(0\) | \(2\) | \(-4\) | \(q-\beta _{4}q^{2}+(-1+2\beta _{3}-\beta _{11})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\) |
144.5.m.b | $32$ | $14.885$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
144.5.m.c | $32$ | $14.885$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{5}^{\mathrm{old}}(144, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)