Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(20\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(24, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 18 | 0 |
Cusp forms | 14 | 14 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(24, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
24.5.h.a | $1$ | $2.481$ | \(\Q\) | \(\Q(\sqrt{-6}) \) | \(-4\) | \(-9\) | \(46\) | \(2\) | \(q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots\) |
24.5.h.b | $1$ | $2.481$ | \(\Q\) | \(\Q(\sqrt{-6}) \) | \(4\) | \(9\) | \(-46\) | \(2\) | \(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\) |
24.5.h.c | $12$ | $2.481$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\) |