Properties

Label 187.2.p
Level 187
Weight 2
Character orbit p
Rep. character \(\chi_{187}(4,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 128
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.p (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 187 \)
Character field: \(\Q(\zeta_{20})\)
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 160 160 0
Cusp forms 128 128 0
Eisenstein series 32 32 0

Trace form

\( 128q - 10q^{3} + 16q^{4} - 2q^{5} - 8q^{6} + O(q^{10}) \) \( 128q - 10q^{3} + 16q^{4} - 2q^{5} - 8q^{6} - 24q^{10} - 40q^{13} + 2q^{14} - 48q^{16} - 18q^{17} - 2q^{20} + 16q^{21} - 70q^{22} - 16q^{23} + 28q^{24} - 22q^{27} + 42q^{28} - 2q^{29} - 44q^{30} - 6q^{31} + 32q^{33} + 44q^{34} + 12q^{35} + 30q^{37} - 80q^{38} + 78q^{39} - 100q^{40} - 56q^{41} + 52q^{44} - 68q^{45} + 14q^{46} - 16q^{47} - 110q^{48} + 84q^{50} + 14q^{51} - 100q^{52} - 20q^{54} - 84q^{55} + 36q^{56} - 48q^{57} - 26q^{58} + 28q^{61} + 108q^{62} - 40q^{63} + 120q^{64} + 28q^{65} - 48q^{67} + 102q^{68} + 24q^{69} + 2q^{71} + 80q^{72} - 30q^{73} - 28q^{74} - 80q^{75} - 104q^{78} + 44q^{79} - 92q^{80} + 140q^{81} - 28q^{82} - 52q^{84} + 76q^{85} + 12q^{86} + 50q^{88} - 32q^{89} + 204q^{90} + 42q^{91} + 2q^{92} + 16q^{95} + 240q^{96} - 34q^{97} + 24q^{98} - 90q^{99} + O(q^{100}) \)

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.p.a \(128\) \(1.493\) None \(0\) \(-10\) \(-2\) \(0\)