Properties

Label 187.2.r
Level 187
Weight 2
Character orbit r
Rep. character \(\chi_{187}(9,\cdot)\)
Character field \(\Q(\zeta_{40})\)
Dimension 256
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.r (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 187 \)
Character field: \(\Q(\zeta_{40})\)
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 320 320 0
Cusp forms 256 256 0
Eisenstein series 64 64 0

Trace form

\( 256q - 12q^{2} - 12q^{3} - 20q^{5} - 12q^{6} - 12q^{7} - 28q^{8} - 36q^{9} + O(q^{10}) \) \( 256q - 12q^{2} - 12q^{3} - 20q^{5} - 12q^{6} - 12q^{7} - 28q^{8} - 36q^{9} - 32q^{10} - 16q^{11} - 32q^{12} - 12q^{14} + 12q^{15} + 16q^{16} + 12q^{17} - 16q^{18} - 12q^{19} - 44q^{20} + 88q^{22} - 48q^{23} - 80q^{24} - 4q^{25} - 12q^{26} - 48q^{27} - 28q^{28} - 12q^{29} + 44q^{31} - 8q^{32} - 56q^{33} - 64q^{34} - 88q^{35} + 56q^{36} - 28q^{37} + 12q^{39} + 120q^{40} - 48q^{41} + 44q^{42} + 8q^{43} - 16q^{44} - 32q^{45} - 44q^{46} + 60q^{48} + 64q^{49} + 32q^{50} - 28q^{51} - 232q^{52} - 20q^{53} + 48q^{54} - 64q^{56} + 128q^{57} + 124q^{58} + 104q^{59} + 4q^{60} + 64q^{61} - 52q^{62} - 12q^{63} - 88q^{65} - 208q^{66} - 96q^{67} + 44q^{68} + 48q^{69} + 92q^{70} - 44q^{71} + 28q^{73} - 12q^{74} + 104q^{75} + 176q^{76} - 148q^{77} - 12q^{79} + 32q^{80} - 72q^{82} - 16q^{83} + 216q^{84} + 80q^{85} - 24q^{86} - 128q^{87} - 32q^{88} - 28q^{90} - 108q^{91} + 76q^{92} + 164q^{93} - 88q^{94} - 32q^{95} - 44q^{96} + 128q^{97} + 144q^{99} + O(q^{100}) \)

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.r.a \(256\) \(1.493\) None \(-12\) \(-12\) \(-20\) \(-12\)