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Properties

Label 855.2.cq
Level $855$
Weight $2$
Character orbit 855.cq
Rep. character $\chi_{855}(71,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $168$
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.cq (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
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 768 168 600
Cusp forms 672 168 504
Eisenstein series 96 0 96

Trace form

\( 168 q - 12 q^{4} + O(q^{10}) \) \( 168 q - 12 q^{4} + 12 q^{10} - 36 q^{13} + 60 q^{16} - 12 q^{19} - 24 q^{28} + 36 q^{34} - 24 q^{40} + 36 q^{43} - 108 q^{49} - 240 q^{52} - 96 q^{58} + 72 q^{61} - 156 q^{64} - 36 q^{67} + 144 q^{70} + 84 q^{73} + 216 q^{76} + 48 q^{79} + 48 q^{82} + 96 q^{85} + 288 q^{88} - 96 q^{97} + O(q^{100}) \)

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.cq.a 855.cq 57.j $168$ $6.827$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)