Defining parameters
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.cb (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 273 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(261\) | ||
Trace bound: | \(12\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1911, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 40 | 32 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 64 | 32 | 32 |
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 \(S_{1}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1911.1.cb.a | $4$ | $0.954$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{4}-\zeta_{12}^{4}q^{9}-q^{12}+\cdots\) |
1911.1.cb.b | $4$ | $0.954$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{4}-\zeta_{12}^{4}q^{9}+q^{12}+\cdots\) |