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Properties

Label 855.2.bx
Level $855$
Weight $2$
Character orbit 855.bx
Rep. character $\chi_{855}(68,\cdot)$
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.bx (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

\( 464 q - 2 q^{3} - 6 q^{5} - 4 q^{6} - 4 q^{7} + O(q^{10}) \) \( 464 q - 2 q^{3} - 6 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} - 8 q^{15} - 424 q^{16} - 18 q^{17} - 24 q^{18} - 12 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{25} - 2 q^{27} - 20 q^{28} + 2 q^{30} - 8 q^{31} - 8 q^{33} + 76 q^{36} - 16 q^{37} - 18 q^{38} + 18 q^{40} + 36 q^{41} + 82 q^{42} - 4 q^{43} + 6 q^{45} - 56 q^{46} + 54 q^{47} - 36 q^{48} - 108 q^{50} + 12 q^{51} + 68 q^{52} - 14 q^{55} - 24 q^{56} - 6 q^{57} - 12 q^{58} + 78 q^{60} + 4 q^{61} + 12 q^{62} - 70 q^{63} - 84 q^{65} - 4 q^{66} - 4 q^{67} - 60 q^{68} + 42 q^{70} + 14 q^{72} - 4 q^{73} + 98 q^{75} + 24 q^{76} - 12 q^{77} - 64 q^{78} - 120 q^{80} - 36 q^{81} + 4 q^{82} - 12 q^{83} - 4 q^{85} + 102 q^{87} + 48 q^{88} - 46 q^{90} - 8 q^{91} - 22 q^{93} + 54 q^{95} + 96 q^{96} - 4 q^{97} - 42 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bx.a 855.bx 855.ax $464$ $6.827$ None \(0\) \(-2\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{12}]$