Properties

Label 861.2.ci
Level 861
Weight 2
Character orbit ci
Rep. character \(\chi_{861}(19,\cdot)\)
Character field \(\Q(\zeta_{120})\)
Dimension 1792
Newforms 1
Sturm bound 224
Trace bound 0

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Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 861.ci (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{120})\)
Newforms: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).

Total New Old
Modular forms 3712 1792 1920
Cusp forms 3456 1792 1664
Eisenstein series 256 0 256

Trace form

\( 1792q + O(q^{10}) \) \( 1792q + 8q^{14} - 224q^{16} + 48q^{19} - 80q^{22} - 72q^{24} - 48q^{26} + 64q^{29} - 16q^{30} - 40q^{32} - 72q^{37} - 72q^{38} + 64q^{42} - 64q^{43} - 192q^{44} - 24q^{46} + 48q^{47} - 160q^{49} + 128q^{50} + 72q^{52} - 16q^{53} + 112q^{56} + 8q^{58} - 64q^{65} + 32q^{67} - 744q^{68} + 160q^{70} + 32q^{71} - 72q^{73} + 56q^{74} - 384q^{75} - 32q^{77} + 96q^{78} - 8q^{79} + 72q^{80} - 576q^{82} + 240q^{84} + 32q^{85} - 88q^{88} - 384q^{89} + 112q^{91} + 216q^{94} + 64q^{95} - 480q^{96} - 40q^{98} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
861.2.ci.a \(1792\) \(6.875\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(861, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)