Properties

Label 37.2.a
Level $37$
Weight $2$
Character orbit 37.a
Rep. character $\chi_{37}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $6$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(37))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

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

\(37\)Dim.
\(+\)\(1\)
\(-\)\(1\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 37
37.2.a.a \(1\) \(0.295\) \(\Q\) None \(-2\) \(-3\) \(-2\) \(-1\) \(+\) \(q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
37.2.a.b \(1\) \(0.295\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)