Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
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: | \(28\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(24, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 26 | 0 |
Cusp forms | 22 | 22 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(24, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
24.7.h.a | $1$ | $5.521$ | \(\Q\) | \(\Q(\sqrt{-6}) \) | \(-8\) | \(27\) | \(-142\) | \(470\) | \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-142q^{5}+\cdots\) |
24.7.h.b | $1$ | $5.521$ | \(\Q\) | \(\Q(\sqrt{-6}) \) | \(8\) | \(-27\) | \(142\) | \(470\) | \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+142q^{5}+\cdots\) |
24.7.h.c | $20$ | $5.521$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-944\) | \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-10+\beta _{3})q^{4}+\cdots\) |