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Properties

Label 619.2.a
Level 619
Weight 2
Character orbit a
Rep. character \(\chi_{619}(1,\cdot)\)
Character field \(\Q\)
Dimension 51
Newforms 2
Sturm bound 103
Trace bound 1

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Defining parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(103\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(619))\).

Total New Old
Modular forms 52 52 0
Cusp forms 51 51 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.

\(619\)Dim.
\(+\)\(21\)
\(-\)\(30\)

Trace form

\( 51q - 4q^{3} + 48q^{4} - 2q^{7} + 6q^{8} + 49q^{9} + O(q^{10}) \) \( 51q - 4q^{3} + 48q^{4} - 2q^{7} + 6q^{8} + 49q^{9} + 6q^{10} - 4q^{11} - 14q^{12} - 2q^{13} - 12q^{14} - 12q^{15} + 46q^{16} - 10q^{17} - 4q^{18} - 16q^{19} + 4q^{20} - 12q^{21} + 12q^{22} - 10q^{23} - 4q^{24} + 51q^{25} - 10q^{26} - 10q^{27} - 12q^{28} + 12q^{29} - 30q^{30} - 6q^{31} + 2q^{32} - 12q^{33} - 2q^{34} + 6q^{35} + 32q^{36} - 4q^{37} + 26q^{38} + 28q^{39} + 14q^{42} - 2q^{43} + 2q^{44} - 6q^{45} - 16q^{46} - 8q^{47} - 34q^{48} + 47q^{49} + 8q^{50} - 8q^{51} + 6q^{52} - 2q^{53} - 32q^{54} + 6q^{55} - 26q^{56} - 32q^{57} + 52q^{58} - 4q^{59} - 56q^{60} - 6q^{61} + 70q^{62} - 46q^{63} + 86q^{64} - 22q^{65} - 30q^{66} + 4q^{67} - 68q^{68} - 24q^{69} + 4q^{70} - 14q^{71} + 18q^{72} - 6q^{73} + 4q^{74} - 50q^{75} - 46q^{76} - 18q^{77} - 20q^{78} + 8q^{79} + 36q^{80} + 11q^{81} + 4q^{82} - 12q^{83} - 56q^{84} - 10q^{85} - 34q^{86} + 24q^{87} + 14q^{88} + 46q^{89} + 58q^{90} - 34q^{91} + 28q^{92} - 30q^{93} - 12q^{94} + 6q^{95} - 56q^{96} + 12q^{97} + 24q^{98} - 46q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 619
619.2.a.a \(21\) \(4.943\) None \(-9\) \(-5\) \(-21\) \(-4\) \(+\)
619.2.a.b \(30\) \(4.943\) None \(9\) \(1\) \(21\) \(2\) \(-\)