Properties

Label 187.2.g
Level 187
Weight 2
Character orbit g
Rep. character \(\chi_{187}(69,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 64
Newforms 6
Sturm bound 36
Trace bound 2

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Defining parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 6 \)
Sturm bound: \(36\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

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

Trace form

\( 64q - 4q^{2} - 2q^{3} - 20q^{4} - 2q^{5} - 4q^{6} - 12q^{7} + 8q^{8} - 18q^{9} + O(q^{10}) \) \( 64q - 4q^{2} - 2q^{3} - 20q^{4} - 2q^{5} - 4q^{6} - 12q^{7} + 8q^{8} - 18q^{9} - 8q^{10} - 8q^{11} + 16q^{12} - 4q^{13} + 18q^{14} - 2q^{15} - 4q^{17} + 22q^{18} - 12q^{19} + 22q^{20} - 8q^{21} - 34q^{22} + 16q^{23} - 44q^{24} - 40q^{25} - 2q^{26} - 26q^{27} + 58q^{28} - 10q^{29} + 28q^{30} + 2q^{31} - 28q^{32} + 4q^{33} + 10q^{35} - 16q^{36} + 6q^{37} + 12q^{38} - 18q^{39} - 44q^{40} + 8q^{41} + 38q^{42} - 24q^{43} - 4q^{44} + 36q^{45} + 6q^{46} - 24q^{47} + 74q^{48} - 6q^{49} - 56q^{50} - 8q^{51} + 48q^{52} + 12q^{53} + 68q^{54} - 66q^{55} - 36q^{56} + 8q^{57} - 10q^{58} - 14q^{59} + 32q^{60} + 12q^{61} - 80q^{62} - 44q^{63} + 28q^{65} - 44q^{66} - 24q^{67} - 12q^{68} + 18q^{69} + 28q^{70} + 18q^{71} - 18q^{72} + 58q^{73} + 16q^{74} + 16q^{75} - 124q^{76} - 14q^{77} + 40q^{78} + 8q^{79} - 12q^{80} - 4q^{81} + 76q^{82} + 44q^{83} - 88q^{84} - 8q^{85} + 44q^{86} - 28q^{87} + 110q^{88} + 8q^{89} + 120q^{90} - 38q^{91} + 58q^{92} - 44q^{93} - 36q^{94} + 56q^{95} + 180q^{96} - 54q^{97} - 160q^{98} + 66q^{99} + O(q^{100}) \)

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.g.a \(4\) \(1.493\) \(\Q(\zeta_{10})\) None \(-2\) \(-5\) \(-5\) \(-8\) \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-2\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
187.2.g.b \(4\) \(1.493\) \(\Q(\zeta_{10})\) None \(2\) \(-4\) \(-1\) \(-8\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
187.2.g.c \(4\) \(1.493\) \(\Q(\zeta_{10})\) None \(5\) \(-1\) \(2\) \(-2\) \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
187.2.g.d \(8\) \(1.493\) 8.0.324000000.3 None \(-4\) \(6\) \(4\) \(2\) \(q+(\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
187.2.g.e \(8\) \(1.493\) 8.0.13140625.1 None \(-1\) \(3\) \(-3\) \(3\) \(q+(-\beta _{1}+\beta _{5})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
187.2.g.f \(36\) \(1.493\) None \(-4\) \(-1\) \(1\) \(1\)