Properties

Label 82.2.a
Level 82
Weight 2
Character orbit a
Rep. character \(\chi_{82}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 21
Trace bound 1

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Defining parameters

Level: \( N \) = \( 82 = 2 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 82.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(82))\).

Total New Old
Modular forms 12 3 9
Cusp forms 9 3 6
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.

\(2\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3q + q^{2} - 2q^{3} + 3q^{4} - 2q^{5} + 2q^{6} - 8q^{7} + q^{8} - q^{9} + O(q^{10}) \) \( 3q + q^{2} - 2q^{3} + 3q^{4} - 2q^{5} + 2q^{6} - 8q^{7} + q^{8} - q^{9} + 2q^{10} - 2q^{11} - 2q^{12} + 4q^{13} - 4q^{15} + 3q^{16} + 2q^{17} - 3q^{18} - 2q^{19} - 2q^{20} + 4q^{21} + 2q^{22} + 2q^{24} + 5q^{25} - 4q^{26} + 4q^{27} - 8q^{28} + 8q^{29} - 12q^{30} - 16q^{31} + q^{32} + 16q^{33} + 6q^{34} + 16q^{35} - q^{36} + 2q^{37} - 14q^{38} - 8q^{39} + 2q^{40} - 3q^{41} - 12q^{42} - 4q^{43} - 2q^{44} - 2q^{45} + 16q^{46} - 2q^{48} + 7q^{49} + 7q^{50} + 20q^{51} + 4q^{52} + 20q^{53} - 4q^{54} - 20q^{55} - 16q^{57} + 8q^{58} - 4q^{60} - 2q^{61} + 3q^{64} - 8q^{65} + 8q^{66} - 10q^{67} + 2q^{68} + 8q^{69} + 4q^{71} - 3q^{72} - 6q^{73} - 2q^{74} + 2q^{75} - 2q^{76} - 4q^{77} + 8q^{78} - 8q^{79} - 2q^{80} - 21q^{81} - q^{82} + 36q^{83} + 4q^{84} - 28q^{85} + 20q^{86} - 16q^{87} + 2q^{88} - 26q^{89} + 2q^{90} - 16q^{91} + 24q^{93} - 8q^{94} - 4q^{95} + 2q^{96} + 2q^{97} - 11q^{98} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(82))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 41
82.2.a.a \(1\) \(0.655\) \(\Q\) None \(-1\) \(-2\) \(-2\) \(-4\) \(+\) \(+\) \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-4q^{7}+\cdots\)
82.2.a.b \(2\) \(0.655\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(82))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(82)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 2}\)