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Properties

Label 855.2.s
Level $855$
Weight $2$
Character orbit 855.s
Rep. character $\chi_{855}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{6})\)
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 248 248 0
Cusp forms 232 232 0
Eisenstein series 16 16 0

Trace form

\( 232 q - 228 q^{4} + q^{5} + 14 q^{6} - 2 q^{9} + O(q^{10}) \) \( 232 q - 228 q^{4} + q^{5} + 14 q^{6} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 26 q^{14} - 6 q^{15} + 212 q^{16} - 8 q^{19} - 19 q^{20} - 8 q^{21} - 22 q^{24} + q^{25} + 8 q^{26} + 26 q^{29} - 17 q^{30} - 4 q^{31} + 16 q^{34} - 13 q^{35} - 22 q^{36} - 18 q^{39} - 8 q^{40} - 38 q^{41} - 4 q^{44} + 23 q^{45} + 4 q^{46} + 88 q^{49} - 18 q^{50} - 50 q^{51} + 30 q^{54} + 3 q^{55} - 44 q^{56} + 46 q^{59} - 3 q^{60} + 2 q^{61} - 176 q^{64} + 34 q^{65} + 18 q^{66} - 2 q^{69} + 18 q^{70} - 66 q^{71} - 56 q^{74} - 58 q^{75} + 12 q^{76} - 4 q^{79} + 26 q^{80} - 82 q^{81} + 2 q^{84} - 22 q^{85} + 120 q^{86} + 44 q^{89} + 7 q^{90} - 18 q^{91} + 4 q^{94} + 3 q^{95} + 86 q^{96} + 22 q^{99} + O(q^{100}) \)

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.s.a 855.s 855.s $232$ $6.827$ None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{6}]$