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Properties

Label 861.2.ci
Level $861$
Weight $2$
Character orbit 861.ci
Rep. character $\chi_{861}(19,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $1792$
Newform subspaces $1$
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: \(\Q(\zeta_{120})\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
861.2.ci.a 861.ci 287.ae $1792$ $6.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{120}]$

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

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