Properties

Label 5077.2.a
Level 5077
Weight 2
Character orbit a
Rep. character \(\chi_{5077}(1,\cdot)\)
Character field \(\Q\)
Dimension 422
Newforms 3
Sturm bound 846
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(846\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5077))\).

Total New Old
Modular forms 423 423 0
Cusp forms 422 422 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.

\(5077\)Dim.
\(+\)\(206\)
\(-\)\(216\)

Trace form

\(422q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 420q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 426q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(422q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 420q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 426q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 412q^{16} \) \(\mathstrut -\mathstrut 12q^{18} \) \(\mathstrut -\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 16q^{24} \) \(\mathstrut +\mathstrut 418q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 440q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 26q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 10q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 402q^{49} \) \(\mathstrut -\mathstrut 10q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 46q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 72q^{56} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 30q^{63} \) \(\mathstrut +\mathstrut 424q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 54q^{66} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 34q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 52q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 72q^{78} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 42q^{80} \) \(\mathstrut +\mathstrut 470q^{81} \) \(\mathstrut -\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 18q^{87} \) \(\mathstrut -\mathstrut 18q^{89} \) \(\mathstrut -\mathstrut 60q^{90} \) \(\mathstrut -\mathstrut 46q^{91} \) \(\mathstrut -\mathstrut 10q^{92} \) \(\mathstrut +\mathstrut 10q^{93} \) \(\mathstrut +\mathstrut 28q^{94} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5077))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5077
5077.2.a.a \(1\) \(40.540\) \(\Q\) None \(-2\) \(-3\) \(-4\) \(-4\) \(+\) \(q-2q^{2}-3q^{3}+2q^{4}-4q^{5}+6q^{6}+\cdots\)
5077.2.a.b \(205\) \(40.540\) None \(-25\) \(-59\) \(-44\) \(-30\) \(+\)
5077.2.a.c \(216\) \(40.540\) None \(25\) \(62\) \(46\) \(30\) \(-\)