Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{15}(16, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 31 | 7 | 24 |
Cusp forms | 25 | 7 | 18 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{15}^{\mathrm{new}}(16, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
16.15.c.a | $1$ | $19.893$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(-152886\) | \(0\) | \(q-152886q^{5}+3^{14}q^{9}-46322630q^{13}+\cdots\) |
16.15.c.b | $2$ | $19.893$ | \(\Q(\sqrt{-3395}) \) | None | \(0\) | \(0\) | \(215700\) | \(0\) | \(q-\beta q^{3}+107850q^{5}+522\beta q^{7}-3039111q^{9}+\cdots\) |
16.15.c.c | $4$ | $19.893$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(0\) | \(0\) | \(-87000\) | \(0\) | \(q+\beta _{1}q^{3}+(-21750+\beta _{3})q^{5}+(245\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{15}^{\mathrm{old}}(16, [\chi])\) into lower level spaces
\( S_{15}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)