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Properties

Label 85.2.d
Level $85$
Weight $2$
Character orbit 85.d
Rep. character $\chi_{85}(16,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 85 = 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 85.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(85, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + 8 q^{13} - 6 q^{16} - 2 q^{17} - 10 q^{18} - 8 q^{21} - 6 q^{25} - 20 q^{26} + 4 q^{30} + 6 q^{32} + 4 q^{33} + 6 q^{34} + 4 q^{35} + 22 q^{36} + 8 q^{38} + 20 q^{42} + 28 q^{43} - 20 q^{47} - 14 q^{49} + 2 q^{50} + 16 q^{51} - 28 q^{53} + 8 q^{55} + 8 q^{59} + 12 q^{60} - 22 q^{64} + 8 q^{66} + 12 q^{67} - 34 q^{68} - 24 q^{70} - 14 q^{72} + 24 q^{76} - 28 q^{77} - 26 q^{81} + 4 q^{83} - 12 q^{85} + 8 q^{86} + 32 q^{87} + 4 q^{89} - 36 q^{93} + 8 q^{94} + 86 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(85, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
85.2.d.a 85.d 17.b $6$ $0.679$ 6.0.350464.1 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{5}q^{3}+(\beta _{1}-\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)