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Properties

Label 861.2.bw
Level $861$
Weight $2$
Character orbit 861.bw
Rep. character $\chi_{861}(236,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $864$
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.bw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
Character field: \(\Q(\zeta_{30})\)
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 928 928 0
Cusp forms 864 864 0
Eisenstein series 64 64 0

Trace form

\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} + O(q^{10}) \) \( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99} + O(q^{100}) \)

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.bw.a 861.bw 861.aw $864$ $6.875$ None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{30}]$