Properties

Label 187.2.j
Level 187
Weight 2
Character orbit j
Rep. character \(\chi_{187}(16,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 64
Newforms 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 187 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(187, [\chi])\).

Total New Old
Modular forms 80 80 0
Cusp forms 64 64 0
Eisenstein series 16 16 0

Trace form

\( 64q - 8q^{2} - 20q^{4} - 4q^{8} + 30q^{9} + O(q^{10}) \) \( 64q - 8q^{2} - 20q^{4} - 4q^{8} + 30q^{9} - 4q^{13} - 34q^{15} - 16q^{16} - 14q^{17} + 10q^{18} - 72q^{21} + 36q^{25} + 22q^{26} - 8q^{30} + 84q^{32} - 44q^{33} - 44q^{34} + 18q^{35} - 32q^{36} - 60q^{38} - 10q^{42} + 32q^{43} + 16q^{47} - 18q^{49} + 4q^{50} - 2q^{51} + 44q^{52} - 16q^{53} + 22q^{55} - 50q^{59} + 68q^{60} - 80q^{64} - 172q^{66} + 40q^{67} + 18q^{68} + 6q^{69} + 128q^{70} + 186q^{72} - 116q^{76} - 30q^{77} + 48q^{81} - 12q^{83} + 68q^{84} - 108q^{85} - 16q^{86} + 92q^{87} - 40q^{89} - 80q^{93} - 188q^{94} + 72q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(187, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
187.2.j.a \(64\) \(1.493\) None \(-8\) \(0\) \(0\) \(0\)