Properties

Label 187.2.a
Level 187
Weight 2
Character orbit a
Rep. character \(\chi_{187}(1,\cdot)\)
Character field \(\Q\)
Dimension 13
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.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(36\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(187))\).

Total New Old
Modular forms 20 13 7
Cusp forms 17 13 4
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(8\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(187))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 17
187.2.a.a \(1\) \(1.493\) \(\Q\) None \(0\) \(1\) \(3\) \(2\) \(-\) \(+\) \(q+q^{3}-2q^{4}+3q^{5}+2q^{7}-2q^{9}+\cdots\)
187.2.a.b \(1\) \(1.493\) \(\Q\) None \(2\) \(0\) \(4\) \(-5\) \(+\) \(-\) \(q+2q^{2}+2q^{4}+4q^{5}-5q^{7}-3q^{9}+\cdots\)
187.2.a.c \(2\) \(1.493\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-4\) \(-4\) \(-\) \(-\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
187.2.a.d \(2\) \(1.493\) \(\Q(\sqrt{17}) \) None \(4\) \(-1\) \(1\) \(3\) \(-\) \(+\) \(q+2q^{2}+(-1+\beta )q^{3}+2q^{4}+(1-\beta )q^{5}+\cdots\)
187.2.a.e \(3\) \(1.493\) 3.3.148.1 None \(-2\) \(-3\) \(-7\) \(0\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
187.2.a.f \(4\) \(1.493\) 4.4.33844.1 None \(1\) \(1\) \(3\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(187))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(187)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)