Defining parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.i (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(48, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 36 | 0 |
Cusp forms | 28 | 28 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(48, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
48.3.i.a | $8$ | $1.308$ | 8.0.629407744.1 | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\) |
48.3.i.b | $20$ | $1.308$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q-\beta _{15}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\) |