Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(16, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 19 | 4 | 15 |
Cusp forms | 13 | 4 | 9 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(16, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
16.9.c.a | $2$ | $6.518$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(0\) | \(-1020\) | \(0\) | \(q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots\) |
16.9.c.b | $2$ | $6.518$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(516\) | \(0\) | \(q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(16, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)