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Properties

Label 861.2.r
Level $861$
Weight $2$
Character orbit 861.r
Rep. character $\chi_{861}(122,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
Character field: \(\Q(\zeta_{6})\)
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 232 232 0
Cusp forms 216 216 0
Eisenstein series 16 16 0

Trace form

\( 216 q + 100 q^{4} + 2 q^{9} + O(q^{10}) \) \( 216 q + 100 q^{4} + 2 q^{9} - 12 q^{10} - 92 q^{16} - 10 q^{18} + 4 q^{21} - 88 q^{25} - 12 q^{31} + 24 q^{33} + 104 q^{36} - 20 q^{37} - 18 q^{39} + 84 q^{40} - 66 q^{42} - 32 q^{43} - 84 q^{45} - 48 q^{46} - 32 q^{49} - 12 q^{51} + 48 q^{57} - 84 q^{61} - 184 q^{64} + 180 q^{66} + 68 q^{72} - 12 q^{73} - 128 q^{78} - 38 q^{81} - 60 q^{82} + 78 q^{87} - 24 q^{91} + O(q^{100}) \)

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.r.a 861.r 861.r $216$ $6.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$