Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 37.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
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.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\) into irreducible Hecke orbits

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 \(0\) \(1\) \(0\) \(-1\) \(-\) \(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)