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Properties

Label 855.2.bm
Level $855$
Weight $2$
Character orbit 855.bm
Rep. character $\chi_{855}(734,\cdot)$
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.bm (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

\( 232 q + 114 q^{4} - 10 q^{6} - 2 q^{9} + O(q^{10}) \) \( 232 q + 114 q^{4} - 10 q^{6} - 2 q^{9} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 15 q^{15} - 106 q^{16} - 8 q^{19} - 21 q^{20} - 6 q^{21} - 8 q^{24} - 2 q^{25} - 12 q^{29} + 21 q^{30} - 15 q^{35} + 22 q^{36} + 2 q^{39} - 12 q^{41} - 15 q^{45} + 88 q^{49} + 12 q^{50} - 84 q^{51} + 42 q^{54} - 7 q^{55} - 12 q^{56} + 60 q^{59} - 54 q^{60} - 4 q^{61} - 224 q^{64} - 54 q^{65} + 6 q^{66} + 42 q^{69} - 18 q^{71} - 108 q^{74} + 54 q^{75} - 6 q^{76} - 6 q^{79} - 12 q^{80} - 54 q^{81} + 30 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{90} - 54 q^{91} - 24 q^{94} + 24 q^{95} + 94 q^{96} - 64 q^{99} + O(q^{100}) \)

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