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Properties

Label 880.2.cg
Level $880$
Weight $2$
Character orbit 880.cg
Rep. character $\chi_{880}(237,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1120$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.cg (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 880 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).

Total New Old
Modular forms 1184 1184 0
Cusp forms 1120 1120 0
Eisenstein series 64 64 0

Trace form

\( 1120 q - 10 q^{2} - 12 q^{3} - 6 q^{5} - 20 q^{6} - 10 q^{8} - 264 q^{9} + O(q^{10}) \) \( 1120 q - 10 q^{2} - 12 q^{3} - 6 q^{5} - 20 q^{6} - 10 q^{8} - 264 q^{9} - 16 q^{11} + 12 q^{12} - 20 q^{13} - 12 q^{15} - 12 q^{16} - 20 q^{17} - 10 q^{18} - 6 q^{20} + 6 q^{22} - 44 q^{26} + 12 q^{27} - 10 q^{28} - 20 q^{30} - 24 q^{31} - 16 q^{33} - 32 q^{34} - 10 q^{35} + 20 q^{36} - 12 q^{37} + 30 q^{38} - 80 q^{40} + 42 q^{42} + 80 q^{44} + 16 q^{45} - 20 q^{46} - 12 q^{47} + 6 q^{48} + 60 q^{50} - 20 q^{51} - 50 q^{52} + 16 q^{56} + 54 q^{58} - 16 q^{59} - 40 q^{60} - 20 q^{61} - 160 q^{62} - 20 q^{63} - 24 q^{66} - 10 q^{68} - 36 q^{69} + 46 q^{70} + 140 q^{72} - 140 q^{74} + 54 q^{75} - 132 q^{78} - 58 q^{80} - 240 q^{81} + 6 q^{82} - 220 q^{83} - 10 q^{85} - 20 q^{86} - 98 q^{88} + 100 q^{90} + 4 q^{91} - 116 q^{92} + 12 q^{93} - 20 q^{95} - 20 q^{96} - 12 q^{97} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
880.2.cg.a 880.cg 880.bg $1120$ $7.027$ None \(-10\) \(-12\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{20}]$