Properties

Label 186.2.a
Level $186$
Weight $2$
Character orbit 186.a
Rep. character $\chi_{186}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 186 = 2 \cdot 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 186.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(186))\).

Total New Old
Modular forms 36 5 31
Cusp forms 29 5 24
Eisenstein series 7 0 7

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

\(2\)\(3\)\(31\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(5\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(186))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 31
186.2.a.a \(1\) \(1.485\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
186.2.a.b \(1\) \(1.485\) \(\Q\) None \(-1\) \(1\) \(3\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-2q^{7}+\cdots\)
186.2.a.c \(1\) \(1.485\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
186.2.a.d \(2\) \(1.485\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(3\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(186))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(186)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 2}\)