Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(10, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6 | 2 | 4 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(10, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
10.4.b.a | $2$ | $0.590$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-10\) | \(0\) | \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\) |