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Properties

Label 861.2.cl
Level $861$
Weight $2$
Character orbit 861.cl
Rep. character $\chi_{861}(11,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $3456$
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.cl (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
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 3712 0
Cusp forms 3456 3456 0
Eisenstein series 256 256 0

Trace form

\( 3456 q - 16 q^{3} - 40 q^{4} - 64 q^{6} - 64 q^{7} - 8 q^{9} + O(q^{10}) \) \( 3456 q - 16 q^{3} - 40 q^{4} - 64 q^{6} - 64 q^{7} - 8 q^{9} - 24 q^{10} + 8 q^{12} - 128 q^{13} - 40 q^{15} - 408 q^{16} - 12 q^{18} - 32 q^{19} - 24 q^{21} - 48 q^{22} - 56 q^{24} - 40 q^{25} - 64 q^{27} - 32 q^{28} - 8 q^{30} - 40 q^{31} - 92 q^{33} - 128 q^{34} + 32 q^{36} - 24 q^{37} - 16 q^{39} - 192 q^{42} - 96 q^{43} - 20 q^{45} - 40 q^{46} + 104 q^{48} - 112 q^{49} + 24 q^{51} - 8 q^{52} - 136 q^{54} - 96 q^{55} - 64 q^{57} - 32 q^{58} - 48 q^{60} + 28 q^{63} - 160 q^{64} - 20 q^{66} - 16 q^{67} - 88 q^{69} - 184 q^{70} - 20 q^{72} - 32 q^{73} - 20 q^{75} - 640 q^{76} + 64 q^{78} - 16 q^{79} + 160 q^{82} + 32 q^{84} - 192 q^{85} - 36 q^{87} - 64 q^{88} - 112 q^{90} - 80 q^{91} + 48 q^{93} - 32 q^{94} + 96 q^{96} - 256 q^{97} - 192 q^{99} + O(q^{100}) \)

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.cl.a 861.cl 861.bl $3456$ $6.875$ None \(0\) \(-16\) \(0\) \(-64\) $\mathrm{SU}(2)[C_{120}]$