Properties

Label 10.8.a
Level 10
Weight 8
Character orbit a
Rep. character \(\chi_{10}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 10.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(10))\).

Total New Old
Modular forms 13 1 12
Cusp forms 9 1 8
Eisenstein series 4 0 4

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

\(2\)\(5\)FrickeDim.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\(q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 125q^{5} \) \(\mathstrut +\mathstrut 224q^{6} \) \(\mathstrut +\mathstrut 104q^{7} \) \(\mathstrut +\mathstrut 512q^{8} \) \(\mathstrut -\mathstrut 1403q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 125q^{5} \) \(\mathstrut +\mathstrut 224q^{6} \) \(\mathstrut +\mathstrut 104q^{7} \) \(\mathstrut +\mathstrut 512q^{8} \) \(\mathstrut -\mathstrut 1403q^{9} \) \(\mathstrut +\mathstrut 1000q^{10} \) \(\mathstrut -\mathstrut 5148q^{11} \) \(\mathstrut +\mathstrut 1792q^{12} \) \(\mathstrut -\mathstrut 8602q^{13} \) \(\mathstrut +\mathstrut 832q^{14} \) \(\mathstrut +\mathstrut 3500q^{15} \) \(\mathstrut +\mathstrut 4096q^{16} \) \(\mathstrut +\mathstrut 20274q^{17} \) \(\mathstrut -\mathstrut 11224q^{18} \) \(\mathstrut +\mathstrut 45500q^{19} \) \(\mathstrut +\mathstrut 8000q^{20} \) \(\mathstrut +\mathstrut 2912q^{21} \) \(\mathstrut -\mathstrut 41184q^{22} \) \(\mathstrut -\mathstrut 72072q^{23} \) \(\mathstrut +\mathstrut 14336q^{24} \) \(\mathstrut +\mathstrut 15625q^{25} \) \(\mathstrut -\mathstrut 68816q^{26} \) \(\mathstrut -\mathstrut 100520q^{27} \) \(\mathstrut +\mathstrut 6656q^{28} \) \(\mathstrut +\mathstrut 231510q^{29} \) \(\mathstrut +\mathstrut 28000q^{30} \) \(\mathstrut -\mathstrut 80128q^{31} \) \(\mathstrut +\mathstrut 32768q^{32} \) \(\mathstrut -\mathstrut 144144q^{33} \) \(\mathstrut +\mathstrut 162192q^{34} \) \(\mathstrut +\mathstrut 13000q^{35} \) \(\mathstrut -\mathstrut 89792q^{36} \) \(\mathstrut +\mathstrut 104654q^{37} \) \(\mathstrut +\mathstrut 364000q^{38} \) \(\mathstrut -\mathstrut 240856q^{39} \) \(\mathstrut +\mathstrut 64000q^{40} \) \(\mathstrut +\mathstrut 584922q^{41} \) \(\mathstrut +\mathstrut 23296q^{42} \) \(\mathstrut -\mathstrut 795532q^{43} \) \(\mathstrut -\mathstrut 329472q^{44} \) \(\mathstrut -\mathstrut 175375q^{45} \) \(\mathstrut -\mathstrut 576576q^{46} \) \(\mathstrut +\mathstrut 425664q^{47} \) \(\mathstrut +\mathstrut 114688q^{48} \) \(\mathstrut -\mathstrut 812727q^{49} \) \(\mathstrut +\mathstrut 125000q^{50} \) \(\mathstrut +\mathstrut 567672q^{51} \) \(\mathstrut -\mathstrut 550528q^{52} \) \(\mathstrut +\mathstrut 1500798q^{53} \) \(\mathstrut -\mathstrut 804160q^{54} \) \(\mathstrut -\mathstrut 643500q^{55} \) \(\mathstrut +\mathstrut 53248q^{56} \) \(\mathstrut +\mathstrut 1274000q^{57} \) \(\mathstrut +\mathstrut 1852080q^{58} \) \(\mathstrut +\mathstrut 246420q^{59} \) \(\mathstrut +\mathstrut 224000q^{60} \) \(\mathstrut +\mathstrut 893942q^{61} \) \(\mathstrut -\mathstrut 641024q^{62} \) \(\mathstrut -\mathstrut 145912q^{63} \) \(\mathstrut +\mathstrut 262144q^{64} \) \(\mathstrut -\mathstrut 1075250q^{65} \) \(\mathstrut -\mathstrut 1153152q^{66} \) \(\mathstrut -\mathstrut 2336836q^{67} \) \(\mathstrut +\mathstrut 1297536q^{68} \) \(\mathstrut -\mathstrut 2018016q^{69} \) \(\mathstrut +\mathstrut 104000q^{70} \) \(\mathstrut -\mathstrut 203688q^{71} \) \(\mathstrut -\mathstrut 718336q^{72} \) \(\mathstrut -\mathstrut 3805702q^{73} \) \(\mathstrut +\mathstrut 837232q^{74} \) \(\mathstrut +\mathstrut 437500q^{75} \) \(\mathstrut +\mathstrut 2912000q^{76} \) \(\mathstrut -\mathstrut 535392q^{77} \) \(\mathstrut -\mathstrut 1926848q^{78} \) \(\mathstrut +\mathstrut 5053040q^{79} \) \(\mathstrut +\mathstrut 512000q^{80} \) \(\mathstrut +\mathstrut 253801q^{81} \) \(\mathstrut +\mathstrut 4679376q^{82} \) \(\mathstrut -\mathstrut 45492q^{83} \) \(\mathstrut +\mathstrut 186368q^{84} \) \(\mathstrut +\mathstrut 2534250q^{85} \) \(\mathstrut -\mathstrut 6364256q^{86} \) \(\mathstrut +\mathstrut 6482280q^{87} \) \(\mathstrut -\mathstrut 2635776q^{88} \) \(\mathstrut +\mathstrut 980010q^{89} \) \(\mathstrut -\mathstrut 1403000q^{90} \) \(\mathstrut -\mathstrut 894608q^{91} \) \(\mathstrut -\mathstrut 4612608q^{92} \) \(\mathstrut -\mathstrut 2243584q^{93} \) \(\mathstrut +\mathstrut 3405312q^{94} \) \(\mathstrut +\mathstrut 5687500q^{95} \) \(\mathstrut +\mathstrut 917504q^{96} \) \(\mathstrut -\mathstrut 5247646q^{97} \) \(\mathstrut -\mathstrut 6501816q^{98} \) \(\mathstrut +\mathstrut 7222644q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(10))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
10.8.a.a \(1\) \(3.124\) \(\Q\) None \(8\) \(28\) \(125\) \(104\) \(-\) \(-\) \(q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(10)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)