Defining parameters
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.p (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 152 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1216, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 4 | 24 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
1216.1.p.a | \(4\) | \(0.607\) | \(\Q(\zeta_{12})\) | \(D_{6}\) | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\) |