Properties

Label 880.2.cy
Level $880$
Weight $2$
Character orbit 880.cy
Rep. character $\chi_{880}(13,\cdot)$
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.cy (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

\( 1120 q - 10 q^{2} - 6 q^{5} - 20 q^{6} - 10 q^{8} + 264 q^{9} + O(q^{10}) \) \( 1120 q - 10 q^{2} - 6 q^{5} - 20 q^{6} - 10 q^{8} + 264 q^{9} - 16 q^{11} - 12 q^{12} - 12 q^{15} - 12 q^{16} - 20 q^{17} - 10 q^{18} - 6 q^{20} - 6 q^{22} - 44 q^{26} - 10 q^{28} - 80 q^{30} - 24 q^{31} - 16 q^{33} + 32 q^{34} - 10 q^{35} + 20 q^{36} + 14 q^{38} + 60 q^{40} - 6 q^{42} - 80 q^{44} - 8 q^{45} - 20 q^{46} - 12 q^{47} - 18 q^{48} - 80 q^{50} - 20 q^{51} - 50 q^{52} - 12 q^{53} + 16 q^{56} - 66 q^{58} + 16 q^{59} - 4 q^{60} - 20 q^{61} + 140 q^{62} - 20 q^{63} - 24 q^{66} - 32 q^{67} - 10 q^{68} + 36 q^{69} - 58 q^{70} + 140 q^{72} + 140 q^{74} - 66 q^{75} + 12 q^{77} - 108 q^{78} - 114 q^{80} - 240 q^{81} - 42 q^{82} - 10 q^{85} - 20 q^{86} - 130 q^{88} + 60 q^{90} + 4 q^{91} - 96 q^{92} - 20 q^{95} - 20 q^{96} - 12 q^{97} + 20 q^{99} + O(q^{100}) \)

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.cy.a 880.cy 880.by $1120$ $7.027$ None \(-10\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{20}]$