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Properties

Label 2883.1.l
Level $2883$
Weight $1$
Character orbit 2883.l
Rep. character $\chi_{2883}(374,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $28$
Newform subspaces $4$
Sturm bound $330$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2883 = 3 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2883.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(330\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2883, [\chi])\).

Total New Old
Modular forms 164 140 24
Cusp forms 36 28 8
Eisenstein series 128 112 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 16 0

Trace form

\( 28 q + q^{3} - 3 q^{4} + 8 q^{7} - 3 q^{9} + O(q^{10}) \) \( 28 q + q^{3} - 3 q^{4} + 8 q^{7} - 3 q^{9} - 4 q^{10} + q^{12} + 2 q^{13} + q^{16} + 4 q^{18} - 3 q^{21} + 12 q^{25} + q^{27} - q^{28} + 12 q^{36} + 2 q^{37} - q^{39} - 4 q^{40} - 3 q^{43} - 4 q^{45} + q^{48} + q^{49} + 4 q^{51} + 2 q^{52} + 2 q^{57} + 2 q^{61} - 6 q^{63} + q^{64} - 6 q^{67} + 4 q^{70} + 4 q^{72} + 2 q^{73} + q^{75} - q^{76} - 3 q^{79} + q^{81} - 4 q^{82} + 2 q^{84} - 16 q^{87} - q^{91} + 3 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2883, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2883.1.l.a 2883.l 93.l $4$ $1.439$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) \(q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+(1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
2883.1.l.b 2883.l 93.l $4$ $1.439$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-2\) \(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
2883.1.l.c 2883.l 93.l $4$ $1.439$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(3\) \(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+(1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
2883.1.l.d 2883.l 93.l $16$ $1.439$ \(\Q(\zeta_{40})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{40}^{14}q^{2}-\zeta_{40}^{11}q^{3}+\zeta_{40}^{10}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2883, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2883, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)