Properties

Label 2891.1.g
Level $2891$
Weight $1$
Character orbit 2891.g
Rep. character $\chi_{2891}(471,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $5$
Sturm bound $280$
Trace bound $17$

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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

\( 10 q - 5 q^{4} - 3 q^{9} + O(q^{10}) \) \( 10 q - 5 q^{4} - 3 q^{9} - 2 q^{15} - 5 q^{16} - 3 q^{17} - 3 q^{25} - 12 q^{27} - 4 q^{29} + 6 q^{36} - 3 q^{45} + 4 q^{51} + 2 q^{53} - 2 q^{57} + 3 q^{59} + q^{60} + 10 q^{64} - 3 q^{68} + 2 q^{71} - 3 q^{75} + 2 q^{79} - q^{81} - 8 q^{85} - 3 q^{87} + q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2891, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2891.1.g.a 2891.g 413.g $2$ $1.443$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-59}) \) 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 2891.g 413.g $2$ $1.443$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-59}) \) 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 2891.g 413.g $2$ $1.443$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-59}) \) 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 2891.g 413.g $2$ $1.443$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-59}) \) 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 2891.g 413.g $2$ $1.443$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-59}) \) 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

\( S_{1}^{\mathrm{old}}(2891, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(413, [\chi])\)\(^{\oplus 2}\)