Defining parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(48, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 8 | 12 |
Cusp forms | 12 | 8 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(48, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
48.2.j.a | $8$ | $0.383$ | 8.0.18939904.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(48, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)