Properties

Label 185.2.a
Level $185$
Weight $2$
Character orbit 185.a
Rep. character $\chi_{185}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $5$
Sturm bound $38$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 185 = 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 185.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(38\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(185))\).

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.

\(5\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(10\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(185))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 37
185.2.a.a \(1\) \(1.477\) \(\Q\) None \(-2\) \(1\) \(-1\) \(-5\) \(+\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-5q^{7}+\cdots\)
185.2.a.b \(1\) \(1.477\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(-\) \(-\) \(q-q^{3}-2q^{4}+q^{5}-3q^{7}-2q^{9}-5q^{11}+\cdots\)
185.2.a.c \(1\) \(1.477\) \(\Q\) None \(1\) \(-2\) \(-1\) \(-2\) \(+\) \(+\) \(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-2q^{7}+\cdots\)
185.2.a.d \(5\) \(1.477\) 5.5.368464.1 None \(0\) \(-1\) \(5\) \(7\) \(-\) \(+\) \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(2-\beta _{1}-\beta _{4})q^{4}+\cdots\)
185.2.a.e \(5\) \(1.477\) 5.5.973904.1 None \(2\) \(3\) \(-5\) \(11\) \(+\) \(-\) \(q+\beta _{4}q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(185))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(185)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)