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Properties

Label 855.2.cc
Level $855$
Weight $2$
Character orbit 855.cc
Rep. character $\chi_{855}(322,\cdot)$
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.cc (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

\( 464 q - 4 q^{5} - 16 q^{6} - 4 q^{7} + O(q^{10}) \) \( 464 q - 4 q^{5} - 16 q^{6} - 4 q^{7} - 8 q^{11} + 200 q^{16} - 40 q^{17} - 36 q^{20} - 20 q^{23} - 4 q^{25} - 64 q^{26} - 32 q^{28} + 12 q^{30} + 32 q^{35} - 64 q^{36} + 34 q^{38} + 84 q^{42} - 4 q^{43} - 112 q^{45} - 24 q^{47} + 24 q^{55} - 6 q^{57} + 12 q^{58} - 8 q^{61} - 32 q^{62} - 68 q^{63} + 80 q^{66} + 76 q^{68} - 16 q^{73} + 24 q^{76} - 12 q^{77} - 120 q^{80} + 64 q^{81} - 32 q^{82} - 4 q^{83} - 4 q^{85} - 44 q^{87} + 20 q^{92} - 108 q^{93} - 44 q^{95} - 224 q^{96} + O(q^{100}) \)

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