Properties

Label 85.2.c
Level 85
Weight 2
Character orbit c
Rep. character \(\chi_{85}(84,\cdot)\)
Character field \(\Q\)
Dimension 8
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 85 \)
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 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\( 8q - 16q^{4} + O(q^{10}) \) \( 8q - 16q^{4} - 16q^{15} + 24q^{16} + 16q^{19} + 8q^{21} - 24q^{26} + 32q^{30} + 32q^{34} - 24q^{35} - 56q^{36} - 16q^{49} - 24q^{50} - 40q^{51} + 8q^{55} + 48q^{59} + 88q^{60} - 48q^{64} + 88q^{66} + 8q^{69} - 8q^{70} - 32q^{76} - 16q^{81} - 72q^{84} + 8q^{85} + 24q^{86} - 24q^{89} - 104q^{94} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
85.2.c.a \(8\) \(0.679\) 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)