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Properties

Label 285.2.z
Level $285$
Weight $2$
Character orbit 285.z
Rep. character $\chi_{285}(41,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $156$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.z (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).

Total New Old
Modular forms 264 156 108
Cusp forms 216 156 60
Eisenstein series 48 0 48

Trace form

\( 156 q + 6 q^{3} + 6 q^{4} + 6 q^{6} - 18 q^{9} + O(q^{10}) \) \( 156 q + 6 q^{3} + 6 q^{4} + 6 q^{6} - 18 q^{9} - 6 q^{10} - 6 q^{13} - 30 q^{16} + 18 q^{19} - 72 q^{22} + 18 q^{24} - 18 q^{27} + 60 q^{28} - 24 q^{30} + 18 q^{34} - 162 q^{36} - 48 q^{39} + 12 q^{40} - 186 q^{42} - 66 q^{43} + 150 q^{48} - 66 q^{49} - 30 q^{51} + 72 q^{52} + 138 q^{54} + 78 q^{57} + 48 q^{58} + 12 q^{61} + 48 q^{63} - 78 q^{64} + 30 q^{66} + 6 q^{67} + 54 q^{69} - 72 q^{70} - 48 q^{72} - 306 q^{73} - 108 q^{76} + 24 q^{78} - 12 q^{79} - 66 q^{81} + 12 q^{82} - 48 q^{85} + 12 q^{87} - 144 q^{88} - 30 q^{90} - 132 q^{91} + 156 q^{96} + 156 q^{97} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(285, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.z.a 285.z 57.j $156$ $2.276$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(285, [\chi])\) into lower level spaces

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