Properties

Label 59.2.a
Level 59
Weight 2
Character orbit a
Rep. character \(\chi_{59}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 59.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(59))\).

Total New Old
Modular forms 6 6 0
Cusp forms 5 5 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.

\(59\)Dim.
\(-\)\(5\)

Trace form

\(5q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 18q^{14} \) \(\mathstrut -\mathstrut 9q^{15} \) \(\mathstrut +\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 6q^{24} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 14q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut +\mathstrut 42q^{36} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 18q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 34q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut q^{45} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 54q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 28q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 26q^{54} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 38q^{56} \) \(\mathstrut -\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 38q^{58} \) \(\mathstrut +\mathstrut 5q^{59} \) \(\mathstrut -\mathstrut 28q^{60} \) \(\mathstrut +\mathstrut 22q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 18q^{64} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 28q^{66} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 3q^{71} \) \(\mathstrut +\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut +\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 14q^{76} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 50q^{80} \) \(\mathstrut -\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut +\mathstrut 28q^{84} \) \(\mathstrut +\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut -\mathstrut 8q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 36q^{94} \) \(\mathstrut +\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 42q^{96} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 24q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 59
59.2.a.a \(5\) \(0.471\) 5.5.138136.1 None \(0\) \(-2\) \(2\) \(2\) \(-\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots\)