Properties

Label 59.2.a
Level $59$
Weight $2$
Character orbit 59.a
Rep. character $\chi_{59}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\) into newform subspaces

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 \(0\) \(-2\) \(2\) \(2\) \(-\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots\)