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Properties

Label 85.2.m
Level $85$
Weight $2$
Character orbit 85.m
Rep. character $\chi_{85}(9,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $24$
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.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(\zeta_{8})\)
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 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

Trace form

\( 24 q - 8 q^{9} + O(q^{10}) \) \( 24 q - 8 q^{9} - 16 q^{10} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 24 q^{19} - 8 q^{20} + 32 q^{24} + 16 q^{25} - 16 q^{26} + 24 q^{29} - 24 q^{31} + 8 q^{34} + 8 q^{35} + 8 q^{36} - 24 q^{39} + 16 q^{40} - 48 q^{41} + 72 q^{44} + 48 q^{45} - 16 q^{46} + 48 q^{49} + 16 q^{50} + 32 q^{54} + 24 q^{56} - 48 q^{59} + 8 q^{60} + 16 q^{61} + 24 q^{65} - 96 q^{66} + 32 q^{69} + 32 q^{70} + 16 q^{71} - 64 q^{74} - 24 q^{76} - 72 q^{79} - 64 q^{80} - 96 q^{84} - 24 q^{85} - 8 q^{91} - 40 q^{94} - 88 q^{95} + 96 q^{96} - 80 q^{99} + O(q^{100}) \)

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.m.a 85.m 85.m $24$ $0.679$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$