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

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

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 \(9\) \(1\) \(21\) \(2\) \(-\)