Properties

Label 5.8.a
Level 5
Weight 8
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 4
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(5))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 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.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3q + 6q^{2} - 28q^{3} + 164q^{4} - 125q^{5} - 344q^{6} - 1744q^{7} + 2280q^{8} + 5671q^{9} + O(q^{10}) \) \( 3q + 6q^{2} - 28q^{3} + 164q^{4} - 125q^{5} - 344q^{6} - 1744q^{7} + 2280q^{8} + 5671q^{9} - 4250q^{10} + 4716q^{11} - 26624q^{12} + 7402q^{13} + 30528q^{14} - 8500q^{15} - 112q^{16} - 39594q^{17} + 29582q^{18} + 12820q^{19} - 3500q^{20} + 9816q^{21} + 103832q^{22} - 111168q^{23} - 171840q^{24} + 46875q^{25} - 111084q^{26} + 305720q^{27} + 53648q^{28} - 153870q^{29} + 211000q^{30} + 149936q^{31} + 100896q^{32} - 449216q^{33} - 281812q^{34} - 193000q^{35} - 211852q^{36} - 12894q^{37} + 702120q^{38} + 589352q^{39} - 75000q^{40} + 732246q^{41} - 1649808q^{42} - 75908q^{43} + 1445808q^{44} - 679625q^{45} - 1485024q^{46} - 502344q^{47} + 1964032q^{48} + 713779q^{49} + 93750q^{50} + 1754536q^{51} - 1415784q^{52} - 3672078q^{53} - 288080q^{54} - 546500q^{55} - 431520q^{56} + 2021840q^{57} + 3386980q^{58} - 2457540q^{59} + 2512000q^{60} + 1333066q^{61} + 4839072q^{62} - 1831968q^{63} - 5032896q^{64} + 40250q^{65} - 6448768q^{66} + 3719156q^{67} - 5744952q^{68} - 1367928q^{69} + 1938000q^{70} + 5725176q^{71} + 1178760q^{72} + 301582q^{73} + 1109508q^{74} - 437500q^{75} - 876240q^{76} + 2894832q^{77} + 7266064q^{78} + 4332080q^{79} - 5102000q^{80} - 7423037q^{81} - 12540308q^{82} - 3652188q^{83} + 4967808q^{84} + 1885750q^{85} + 17787096q^{86} - 20541640q^{87} + 10712160q^{88} + 8036190q^{89} - 4107250q^{90} - 11701424q^{91} - 6316944q^{92} + 14003664q^{93} + 11417168q^{94} - 8087500q^{95} + 4714496q^{96} - 272394q^{97} - 38814042q^{98} + 2910812q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.8.a.a \(1\) \(1.562\) \(\Q\) None \(-14\) \(-48\) \(125\) \(-1644\) \(-\) \(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b \(2\) \(1.562\) \(\Q(\sqrt{19}) \) None \(20\) \(20\) \(-250\) \(-100\) \(+\) \(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)