Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(24, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 6 | 22 |
Cusp forms | 20 | 6 | 14 |
Eisenstein series | 8 | 0 | 8 |
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.e.a | $6$ | $5.521$ | 6.0.1173604352.2 | None | \(0\) | \(-10\) | \(0\) | \(156\) | \(q+(-2+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3^{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(24, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)