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

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

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 \(20\) \(20\) \(-250\) \(-100\) \(+\) \(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)