Defining parameters
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(15, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12 | 4 | 8 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
15.3.f.a | $4$ | $0.409$ | \(\Q(i, \sqrt{6})\) | None | \(-4\) | \(0\) | \(-4\) | \(4\) | \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\) |