Defining parameters
Level: | \( N \) | \(=\) | \( 612 = 2^{2} \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 612.v (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 68 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(108\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(612, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 16 | 24 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 32 | 8 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(612, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
612.1.v.a | $4$ | $0.305$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1+\zeta_{8})q^{5}+\cdots\) |
612.1.v.b | $4$ | $0.305$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1-\zeta_{8})q^{5}-\zeta_{8}q^{8}+\cdots\) |