Defining parameters
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(40, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 20 | 12 |
Cusp forms | 28 | 20 | 8 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(40, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
40.6.d.a | $20$ | $6.415$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(2\) | \(0\) | \(0\) | \(-196\) | \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+\beta _{5}q^{5}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(40, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)