Properties

Label 62.2.a
Level 62
Weight 2
Character orbit a
Rep. character \(\chi_{62}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 16
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 62 = 2 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 62.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(62))\).

Total New Old
Modular forms 10 3 7
Cusp forms 7 3 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.

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

Trace form

\( 3q - q^{2} + 2q^{3} + 3q^{4} - 2q^{5} - 2q^{6} + 4q^{7} - q^{8} - q^{9} + O(q^{10}) \) \( 3q - q^{2} + 2q^{3} + 3q^{4} - 2q^{5} - 2q^{6} + 4q^{7} - q^{8} - q^{9} - 2q^{10} - 6q^{11} + 2q^{12} - 4q^{14} - 12q^{15} + 3q^{16} - 6q^{17} - 5q^{18} - 4q^{19} - 2q^{20} + 4q^{21} + 6q^{22} + 8q^{23} - 2q^{24} + 13q^{25} + 4q^{26} + 8q^{27} + 4q^{28} - 4q^{29} + 12q^{30} + q^{31} - q^{32} - 6q^{34} - q^{36} + 20q^{37} + 12q^{38} - 20q^{39} - 2q^{40} + 6q^{41} - 4q^{42} + 6q^{43} - 6q^{44} - 18q^{45} + 8q^{46} + 4q^{47} + 2q^{48} - 13q^{49} - 15q^{50} + 12q^{51} - 8q^{54} - 12q^{55} - 4q^{56} - 8q^{57} + 8q^{58} - 24q^{59} - 12q^{60} - 8q^{61} - 3q^{62} + 4q^{63} + 3q^{64} + 32q^{65} + 4q^{67} - 6q^{68} + 8q^{71} - 5q^{72} - 10q^{73} + 14q^{75} - 4q^{76} - 12q^{77} + 20q^{78} - 4q^{79} - 2q^{80} + 11q^{81} - 18q^{82} + 14q^{83} + 4q^{84} - 12q^{85} + 10q^{86} + 12q^{87} + 6q^{88} + 6q^{89} + 30q^{90} - 4q^{91} + 8q^{92} + 2q^{93} - 20q^{94} - 8q^{95} - 2q^{96} + 6q^{97} - q^{98} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(62))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 31
62.2.a.a \(1\) \(0.495\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
62.2.a.b \(2\) \(0.495\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(4\) \(+\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(62))\) into lower level spaces

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