Defining parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(48, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 9 | 29 |
Cusp forms | 26 | 7 | 19 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(48, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
48.5.e.a | $1$ | $4.962$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-9\) | \(0\) | \(94\) | \(q-9q^{3}+94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\) |
48.5.e.b | $2$ | $4.962$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(6\) | \(0\) | \(-52\) | \(q+(3+\beta )q^{3}+2\beta q^{5}-26q^{7}+(-63+\cdots)q^{9}+\cdots\) |
48.5.e.c | $4$ | $4.962$ | \(\Q(\sqrt{-2}, \sqrt{13})\) | None | \(0\) | \(4\) | \(0\) | \(-24\) | \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(48, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)