Properties

Label 855.2.bv
Level $855$
Weight $2$
Character orbit 855.bv
Rep. character $\chi_{855}(88,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $464$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(855, [\chi])\).

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 6 q^{3} + 2 q^{5} - 4 q^{6} - 4 q^{7} + O(q^{10}) \) \( 464 q - 6 q^{3} + 2 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{10} - 8 q^{11} + 30 q^{12} + 12 q^{15} - 424 q^{16} - 10 q^{17} - 12 q^{18} + 12 q^{20} - 12 q^{21} + 18 q^{22} - 20 q^{23} + 2 q^{25} - 64 q^{26} + 18 q^{27} - 20 q^{28} - 18 q^{30} - 24 q^{33} + 8 q^{35} + 44 q^{36} - 86 q^{38} - 6 q^{40} - 12 q^{41} + 18 q^{42} - 4 q^{43} + 26 q^{45} - 18 q^{47} + 12 q^{48} + 36 q^{51} - 12 q^{53} + 6 q^{55} + 96 q^{56} - 6 q^{57} - 12 q^{58} - 78 q^{60} + 4 q^{61} - 8 q^{62} + 10 q^{63} + 72 q^{65} + 92 q^{66} - 44 q^{68} - 6 q^{70} - 24 q^{71} - 30 q^{72} - 4 q^{73} - 78 q^{75} + 24 q^{76} + 84 q^{77} - 60 q^{78} - 60 q^{80} + 28 q^{81} + 4 q^{82} - 4 q^{83} - 4 q^{85} - 86 q^{87} + 36 q^{88} - 6 q^{90} - 24 q^{91} + 116 q^{92} - 78 q^{93} - 74 q^{95} - 32 q^{96} + 6 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(855, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.2.bv.a 855.bv 855.av $464$ $6.827$ None \(0\) \(-6\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{12}]$