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Properties

Label 285.2.x
Level $285$
Weight $2$
Character orbit 285.x
Rep. character $\chi_{285}(88,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
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.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
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 176 80 96
Cusp forms 144 80 64
Eisenstein series 32 0 32

Trace form

\( 80 q + 4 q^{5} + 4 q^{6} + 8 q^{7} + O(q^{10}) \) \( 80 q + 4 q^{5} + 4 q^{6} + 8 q^{7} - 16 q^{11} + 28 q^{16} - 4 q^{17} - 80 q^{20} - 24 q^{21} - 24 q^{22} + 8 q^{23} + 4 q^{25} - 32 q^{26} - 28 q^{28} - 16 q^{30} + 12 q^{32} + 12 q^{33} - 44 q^{35} - 36 q^{36} - 96 q^{38} + 132 q^{40} + 72 q^{41} - 12 q^{47} - 24 q^{51} - 36 q^{53} + 8 q^{55} + 24 q^{57} + 40 q^{58} - 48 q^{60} - 40 q^{61} - 4 q^{62} + 4 q^{63} + 48 q^{66} + 88 q^{68} - 24 q^{70} - 36 q^{72} + 40 q^{73} + 24 q^{76} - 40 q^{77} - 120 q^{78} + 24 q^{80} + 40 q^{81} - 36 q^{82} - 8 q^{83} + 80 q^{85} + 48 q^{86} - 64 q^{87} - 36 q^{90} + 72 q^{91} + 12 q^{92} - 48 q^{93} + 48 q^{95} + 88 q^{96} + 12 q^{97} + 96 q^{98} + O(q^{100}) \)

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.x.a 285.x 95.l $80$ $2.276$ None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(285, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)