Properties

Label 5.4.a
Level 5
Weight 4
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(5))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(5\)Dim.
\(+\)\(1\)

Trace form

\(q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut -\mathstrut 38q^{13} \) \(\mathstrut -\mathstrut 24q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 26q^{17} \) \(\mathstrut +\mathstrut 92q^{18} \) \(\mathstrut +\mathstrut 100q^{19} \) \(\mathstrut -\mathstrut 40q^{20} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 128q^{22} \) \(\mathstrut -\mathstrut 78q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut +\mathstrut 152q^{26} \) \(\mathstrut -\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 48q^{28} \) \(\mathstrut -\mathstrut 50q^{29} \) \(\mathstrut +\mathstrut 40q^{30} \) \(\mathstrut -\mathstrut 108q^{31} \) \(\mathstrut +\mathstrut 256q^{32} \) \(\mathstrut +\mathstrut 64q^{33} \) \(\mathstrut -\mathstrut 104q^{34} \) \(\mathstrut -\mathstrut 30q^{35} \) \(\mathstrut -\mathstrut 184q^{36} \) \(\mathstrut +\mathstrut 266q^{37} \) \(\mathstrut -\mathstrut 400q^{38} \) \(\mathstrut -\mathstrut 76q^{39} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 48q^{42} \) \(\mathstrut +\mathstrut 442q^{43} \) \(\mathstrut +\mathstrut 256q^{44} \) \(\mathstrut +\mathstrut 115q^{45} \) \(\mathstrut +\mathstrut 312q^{46} \) \(\mathstrut -\mathstrut 514q^{47} \) \(\mathstrut -\mathstrut 128q^{48} \) \(\mathstrut -\mathstrut 307q^{49} \) \(\mathstrut -\mathstrut 100q^{50} \) \(\mathstrut +\mathstrut 52q^{51} \) \(\mathstrut -\mathstrut 304q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 400q^{54} \) \(\mathstrut -\mathstrut 160q^{55} \) \(\mathstrut +\mathstrut 200q^{57} \) \(\mathstrut +\mathstrut 200q^{58} \) \(\mathstrut +\mathstrut 500q^{59} \) \(\mathstrut -\mathstrut 80q^{60} \) \(\mathstrut -\mathstrut 518q^{61} \) \(\mathstrut +\mathstrut 432q^{62} \) \(\mathstrut -\mathstrut 138q^{63} \) \(\mathstrut -\mathstrut 512q^{64} \) \(\mathstrut +\mathstrut 190q^{65} \) \(\mathstrut -\mathstrut 256q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut +\mathstrut 208q^{68} \) \(\mathstrut -\mathstrut 156q^{69} \) \(\mathstrut +\mathstrut 120q^{70} \) \(\mathstrut +\mathstrut 412q^{71} \) \(\mathstrut -\mathstrut 878q^{73} \) \(\mathstrut -\mathstrut 1064q^{74} \) \(\mathstrut +\mathstrut 50q^{75} \) \(\mathstrut +\mathstrut 800q^{76} \) \(\mathstrut +\mathstrut 192q^{77} \) \(\mathstrut +\mathstrut 304q^{78} \) \(\mathstrut +\mathstrut 600q^{79} \) \(\mathstrut +\mathstrut 320q^{80} \) \(\mathstrut +\mathstrut 421q^{81} \) \(\mathstrut -\mathstrut 88q^{82} \) \(\mathstrut +\mathstrut 282q^{83} \) \(\mathstrut +\mathstrut 96q^{84} \) \(\mathstrut -\mathstrut 130q^{85} \) \(\mathstrut -\mathstrut 1768q^{86} \) \(\mathstrut -\mathstrut 100q^{87} \) \(\mathstrut -\mathstrut 150q^{89} \) \(\mathstrut -\mathstrut 460q^{90} \) \(\mathstrut -\mathstrut 228q^{91} \) \(\mathstrut -\mathstrut 624q^{92} \) \(\mathstrut -\mathstrut 216q^{93} \) \(\mathstrut +\mathstrut 2056q^{94} \) \(\mathstrut -\mathstrut 500q^{95} \) \(\mathstrut +\mathstrut 512q^{96} \) \(\mathstrut +\mathstrut 386q^{97} \) \(\mathstrut +\mathstrut 1228q^{98} \) \(\mathstrut -\mathstrut 736q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.4.a.a \(1\) \(0.295\) \(\Q\) None \(-4\) \(2\) \(-5\) \(6\) \(+\) \(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)