Properties

Label 65.2.a
Level 65
Weight 2
Character orbit a
Rep. character \(\chi_{65}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 3
Sturm bound 14
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(14\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(65))\).

Total New Old
Modular forms 8 5 3
Cusp forms 5 5 0
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.

\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5q - 3q^{2} + 3q^{4} - q^{5} + 4q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( 5q - 3q^{2} + 3q^{4} - q^{5} + 4q^{7} - 3q^{8} + q^{9} - q^{10} - 4q^{12} - q^{13} - 8q^{14} - 5q^{16} - 2q^{17} - 11q^{18} - 4q^{19} + q^{20} + 4q^{21} - 4q^{22} + 4q^{24} + 5q^{25} + 3q^{26} + 12q^{27} + 28q^{28} - 10q^{29} + 8q^{30} + 12q^{31} + q^{32} - 20q^{33} + 6q^{34} + 4q^{35} - q^{36} - 10q^{37} + 24q^{38} + 4q^{39} - 9q^{40} - 18q^{41} - 4q^{42} + 12q^{43} + 4q^{44} - 5q^{45} + 8q^{46} + 12q^{47} - 8q^{48} + 13q^{49} - 3q^{50} - 24q^{51} + q^{52} - 10q^{53} - 20q^{54} + 8q^{55} - 32q^{56} - 4q^{57} + 2q^{58} + 12q^{59} - 12q^{60} - 10q^{61} - 8q^{62} - 4q^{63} - 5q^{64} - 3q^{65} + 40q^{66} - 16q^{67} + 10q^{68} + 8q^{69} - 16q^{70} + 16q^{71} + 21q^{72} - 14q^{73} + 26q^{74} - 4q^{77} - 12q^{78} - 8q^{79} + 17q^{80} - 19q^{81} - 2q^{82} - 40q^{83} - 28q^{84} - 6q^{85} + 36q^{86} + 12q^{87} - 16q^{88} + 2q^{89} + 15q^{90} + 4q^{91} + 20q^{92} + 60q^{93} + 8q^{94} + 12q^{95} + 32q^{96} - 2q^{97} - 51q^{98} - 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(65))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 13
65.2.a.a \(1\) \(0.519\) \(\Q\) None \(-1\) \(-2\) \(-1\) \(-4\) \(+\) \(+\) \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
65.2.a.b \(2\) \(0.519\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
65.2.a.c \(2\) \(0.519\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(4\) \(+\) \(-\) \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}-q^{5}+(-3+\cdots)q^{6}+\cdots\)