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Properties

Label 855.2.co
Level $855$
Weight $2$
Character orbit 855.co
Rep. character $\chi_{855}(299,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
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.co (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{18})\)
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 744 744 0
Cusp forms 696 696 0
Eisenstein series 48 48 0

Trace form

\( 696 q - 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{9} + O(q^{10}) \) \( 696 q - 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{9} - 12 q^{10} - 18 q^{11} - 18 q^{14} + 15 q^{15} - 30 q^{16} - 24 q^{19} - 18 q^{20} + 24 q^{21} + 78 q^{24} - 3 q^{25} + 72 q^{26} - 18 q^{29} - 24 q^{30} - 18 q^{31} + 12 q^{34} + 45 q^{35} - 24 q^{36} - 36 q^{39} + 24 q^{40} - 18 q^{41} - 72 q^{44} - 30 q^{45} - 36 q^{46} - 564 q^{49} + 63 q^{50} + 6 q^{51} - 60 q^{54} + 3 q^{55} + 126 q^{56} - 126 q^{59} + 45 q^{60} - 6 q^{61} + 234 q^{64} - 9 q^{65} - 216 q^{66} - 18 q^{69} + 18 q^{70} + 72 q^{74} - 6 q^{76} - 6 q^{79} - 126 q^{80} - 18 q^{84} - 3 q^{85} - 18 q^{86} - 15 q^{90} + 18 q^{91} - 9 q^{95} - 174 q^{99} + O(q^{100}) \)

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.co.a 855.co 855.bo $696$ $6.827$ None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{18}]$