Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
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: | \(14\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(16, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 3 | 12 |
Cusp forms | 9 | 3 | 6 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(16, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
16.7.c.a | $1$ | $3.681$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(234\) | \(0\) | \(q+234q^{5}+3^{6}q^{9}-4070q^{13}-990q^{17}+\cdots\) |
16.7.c.b | $2$ | $3.681$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-300\) | \(0\) | \(q-\zeta_{6}q^{3}-150q^{5}-22\zeta_{6}q^{7}-39q^{9}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(16, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)