Defining parameters
Level: | \( N \) | \(=\) | \( 2891 = 7^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2891.g (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 413 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(280\) | ||
Trace bound: | \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2891, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 18 | 20 |
Cusp forms | 22 | 10 | 12 |
Eisenstein series | 16 | 8 | 8 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2891, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2891.1.g.a | $2$ | $1.443$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{12}+\cdots\) |
2891.1.g.b | $2$ | $1.443$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{12}+\cdots\) |
2891.1.g.c | $2$ | $1.443$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(-1\) | \(2\) | \(0\) | \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{12}+\cdots\) |
2891.1.g.d | $2$ | $1.443$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(1\) | \(1\) | \(0\) | \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{12}+\cdots\) |
2891.1.g.e | $2$ | $1.443$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(2\) | \(-1\) | \(0\) | \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2891, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2891, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(413, [\chi])\)\(^{\oplus 2}\)