Defining parameters
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(12, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6 | 2 | 4 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
12.3.d.a | \(2\) | \(0.327\) | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(-4\) | \(0\) | \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\) |