↑

Properties

Label 855.2.dc
Level $855$
Weight $2$
Character orbit 855.dc
Rep. character $\chi_{855}(454,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.dc (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

\( 696 q - 6 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + O(q^{10}) \) \( 696 q - 6 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 12 q^{10} - 12 q^{11} - 30 q^{14} - 36 q^{15} + 6 q^{16} - 24 q^{19} - 6 q^{20} - 30 q^{21} - 3 q^{25} - 36 q^{26} - 6 q^{29} - 45 q^{30} - 12 q^{31} + 30 q^{34} + 21 q^{35} - 24 q^{36} - 12 q^{39} - 45 q^{40} - 6 q^{41} - 48 q^{44} + 33 q^{45} - 12 q^{46} + 282 q^{49} - 54 q^{50} + 6 q^{51} + 48 q^{54} - 27 q^{55} - 198 q^{56} - 102 q^{59} + 69 q^{60} - 6 q^{61} + 270 q^{64} + 54 q^{65} - 72 q^{66} - 6 q^{69} - 45 q^{70} - 60 q^{71} + 90 q^{74} + 72 q^{75} - 6 q^{76} - 6 q^{79} - 78 q^{80} + 120 q^{81} - 162 q^{84} - 3 q^{85} - 60 q^{86} - 24 q^{89} + 27 q^{90} + 18 q^{91} - 12 q^{94} + 9 q^{95} - 192 q^{96} - 132 q^{99} + O(q^{100}) \)

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.dc.a 855.dc 855.cc $696$ $6.827$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{18}]$