Defining parameters
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(40, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 4 | 18 |
Cusp forms | 14 | 4 | 10 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(40, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
40.4.c.a | $4$ | $2.360$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(40, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(40, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)