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Properties

Label 855.2.ce
Level $855$
Weight $2$
Character orbit 855.ce
Rep. character $\chi_{855}(202,\cdot)$
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.ce (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

\( 464 q - 6 q^{2} - 6 q^{3} - 4 q^{5} - 4 q^{6} - 4 q^{7} + O(q^{10}) \) \( 464 q - 6 q^{2} - 6 q^{3} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{10} - 8 q^{11} - 30 q^{12} - 6 q^{13} - 6 q^{15} + 212 q^{16} - 10 q^{17} + 12 q^{18} + 12 q^{20} - 12 q^{21} + 10 q^{23} - 4 q^{25} - 64 q^{26} - 18 q^{27} - 20 q^{28} - 18 q^{30} - 30 q^{32} - 6 q^{33} + 8 q^{35} - 4 q^{36} + 46 q^{38} - 78 q^{42} + 2 q^{43} + 26 q^{45} + 36 q^{47} + 30 q^{48} + 36 q^{51} - 18 q^{52} - 12 q^{53} + 6 q^{55} - 96 q^{56} - 78 q^{57} - 12 q^{58} - 6 q^{60} - 8 q^{61} - 8 q^{62} - 68 q^{63} - 72 q^{65} - 100 q^{66} - 6 q^{67} - 44 q^{68} - 24 q^{71} - 138 q^{72} - 4 q^{73} + 78 q^{75} - 60 q^{76} + 84 q^{77} - 48 q^{78} - 60 q^{80} + 4 q^{81} + 4 q^{82} - 4 q^{83} + 2 q^{85} + 96 q^{86} - 86 q^{87} - 36 q^{88} + 6 q^{90} - 24 q^{91} - 58 q^{92} + 24 q^{93} + 112 q^{95} - 32 q^{96} - 6 q^{97} + 6 q^{98} + O(q^{100}) \)

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