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Properties

Label 880.2.ci
Level $880$
Weight $2$
Character orbit 880.ci
Rep. character $\chi_{880}(19,\cdot)$
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.ci (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

\( 1120 q - 12 q^{4} - 6 q^{5} - 20 q^{6} + O(q^{10}) \) \( 1120 q - 12 q^{4} - 6 q^{5} - 20 q^{6} - 16 q^{11} - 4 q^{14} - 12 q^{16} - 20 q^{19} - 6 q^{20} - 20 q^{24} - 40 q^{26} - 20 q^{29} - 50 q^{30} - 16 q^{34} - 10 q^{35} - 44 q^{36} - 40 q^{39} - 10 q^{40} - 44 q^{44} - 24 q^{45} + 20 q^{46} - 256 q^{49} - 10 q^{50} - 20 q^{51} - 48 q^{55} - 24 q^{56} - 28 q^{59} - 46 q^{60} - 20 q^{61} - 36 q^{64} - 28 q^{66} + 24 q^{69} - 72 q^{70} + 8 q^{71} - 20 q^{74} - 42 q^{75} - 32 q^{80} + 192 q^{81} + 120 q^{84} - 10 q^{85} - 4 q^{86} - 260 q^{90} + 60 q^{91} + 120 q^{94} - 20 q^{96} - 96 q^{99} + O(q^{100}) \)

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