Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(24, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 14 | 0 |
Cusp forms | 10 | 10 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(24, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
24.4.f.a | $2$ | $1.416$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-2}) \) | \(0\) | \(10\) | \(0\) | \(0\) | \(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\) |
24.4.f.b | $8$ | $1.416$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(-12\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\) |