Properties

Label 31.2.a
Level 31
Weight 2
Character orbit a
Rep. character \(\chi_{31}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 5
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 31.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(31))\).

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.

\(31\)Dim.
\(-\)\(2\)

Trace form

\( 2q + q^{2} - 2q^{3} - q^{4} + 2q^{5} - 6q^{6} - 4q^{7} + 6q^{9} + O(q^{10}) \) \( 2q + q^{2} - 2q^{3} - q^{4} + 2q^{5} - 6q^{6} - 4q^{7} + 6q^{9} + q^{10} + 4q^{11} - 4q^{12} - 2q^{13} + 3q^{14} - 2q^{15} - 3q^{16} + 6q^{17} + 13q^{18} - q^{20} - 6q^{21} + 2q^{22} - 2q^{23} + 10q^{24} - 8q^{25} - 6q^{26} - 20q^{27} + 7q^{28} + 10q^{29} - 6q^{30} + 2q^{31} - 9q^{32} - 4q^{33} - 2q^{34} - 4q^{35} + 7q^{36} - 4q^{37} - 5q^{38} + 12q^{39} + 14q^{41} + 2q^{42} - 2q^{43} - 2q^{44} + 6q^{45} + 14q^{46} - 4q^{47} + 18q^{48} + 4q^{49} - 4q^{50} + 4q^{51} - 4q^{52} - 12q^{53} - 20q^{54} + 4q^{55} - 10q^{56} + 10q^{57} - 4q^{60} - 6q^{61} + q^{62} + 8q^{63} + 4q^{64} - 2q^{65} - 12q^{66} + 16q^{67} - 8q^{68} - 28q^{69} + 3q^{70} + 4q^{71} - 20q^{72} + 8q^{73} - 2q^{74} + 8q^{75} - 5q^{76} - 8q^{77} + 16q^{78} - 10q^{79} - 3q^{80} + 22q^{81} + 7q^{82} - 12q^{83} + 8q^{84} + 6q^{85} + 4q^{86} + 10q^{89} + 13q^{90} - 6q^{91} + 16q^{92} - 2q^{93} + 8q^{94} + 4q^{96} - 14q^{97} - 18q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 31
31.2.a.a \(2\) \(0.248\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(2\) \(-4\) \(-\) \(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)