Defining parameters
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(12, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 16 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(12, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
12.8.b.a | $4$ | $3.749$ | \(\Q(\sqrt{3}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(-3\beta _{2}+3\beta _{3})q^{3}+(88+4\beta _{1}+\cdots)q^{4}+\cdots\) |
12.8.b.b | $8$ | $3.749$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-41+\beta _{2}+\cdots)q^{4}+\cdots\) |