Defining parameters
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.s (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 273 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(261\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1911, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 50 | 22 | 28 |
Cusp forms | 18 | 6 | 12 |
Eisenstein series | 32 | 16 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 2 | 4 | 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.s.a | $2$ | $0.954$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(0\) | \(0\) | \(q+\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{12}+\cdots\) |
1911.1.s.b | $4$ | $0.954$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{4}q^{6}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)