Defining parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(48, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 70 | 17 | 53 |
Cusp forms | 58 | 15 | 43 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(48, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
48.9.e.a | $1$ | $19.554$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-81\) | \(0\) | \(-4034\) | \(q-3^{4}q^{3}-4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots\) |
48.9.e.b | $2$ | $19.554$ | \(\Q(\sqrt{-14}) \) | None | \(0\) | \(-90\) | \(0\) | \(3500\) | \(q+(-45-3\beta )q^{3}+10\beta q^{5}+1750q^{7}+\cdots\) |
48.9.e.c | $2$ | $19.554$ | \(\Q(\sqrt{-110}) \) | None | \(0\) | \(102\) | \(0\) | \(6188\) | \(q+(51+\beta )q^{3}+18\beta q^{5}+3094q^{7}+\cdots\) |
48.9.e.d | $2$ | $19.554$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(126\) | \(0\) | \(-5572\) | \(q+(63-3\beta )q^{3}+34\beta q^{5}-2786q^{7}+\cdots\) |
48.9.e.e | $8$ | $19.554$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(-56\) | \(0\) | \(-1584\) | \(q+(-7-\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(-198+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(48, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)