Properties

Label 7.10.a
Level 7
Weight 10
Character orbit a
Rep. character \(\chi_{7}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 7.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(7))\).

Total New Old
Modular forms 7 5 2
Cusp forms 5 5 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.

\(7\)Dim.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 937q^{4} \) \(\mathstrut -\mathstrut 684q^{5} \) \(\mathstrut +\mathstrut 926q^{6} \) \(\mathstrut +\mathstrut 2401q^{7} \) \(\mathstrut +\mathstrut 16671q^{8} \) \(\mathstrut -\mathstrut 14963q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 937q^{4} \) \(\mathstrut -\mathstrut 684q^{5} \) \(\mathstrut +\mathstrut 926q^{6} \) \(\mathstrut +\mathstrut 2401q^{7} \) \(\mathstrut +\mathstrut 16671q^{8} \) \(\mathstrut -\mathstrut 14963q^{9} \) \(\mathstrut -\mathstrut 54476q^{10} \) \(\mathstrut +\mathstrut 31872q^{11} \) \(\mathstrut -\mathstrut 54250q^{12} \) \(\mathstrut -\mathstrut 46312q^{13} \) \(\mathstrut +\mathstrut 64827q^{14} \) \(\mathstrut -\mathstrut 106832q^{15} \) \(\mathstrut +\mathstrut 482209q^{16} \) \(\mathstrut +\mathstrut 552774q^{17} \) \(\mathstrut +\mathstrut 58775q^{18} \) \(\mathstrut -\mathstrut 702574q^{19} \) \(\mathstrut -\mathstrut 1448328q^{20} \) \(\mathstrut +\mathstrut 408170q^{21} \) \(\mathstrut -\mathstrut 1669160q^{22} \) \(\mathstrut +\mathstrut 2663760q^{23} \) \(\mathstrut +\mathstrut 1851666q^{24} \) \(\mathstrut +\mathstrut 5154943q^{25} \) \(\mathstrut -\mathstrut 12912480q^{26} \) \(\mathstrut -\mathstrut 2246732q^{27} \) \(\mathstrut +\mathstrut 5226977q^{28} \) \(\mathstrut -\mathstrut 5921766q^{29} \) \(\mathstrut +\mathstrut 12149072q^{30} \) \(\mathstrut +\mathstrut 5336700q^{31} \) \(\mathstrut +\mathstrut 26506527q^{32} \) \(\mathstrut -\mathstrut 35900576q^{33} \) \(\mathstrut -\mathstrut 6228318q^{34} \) \(\mathstrut +\mathstrut 9104592q^{35} \) \(\mathstrut -\mathstrut 41009095q^{36} \) \(\mathstrut +\mathstrut 32131170q^{37} \) \(\mathstrut +\mathstrut 46984530q^{38} \) \(\mathstrut +\mathstrut 38427256q^{39} \) \(\mathstrut -\mathstrut 115269264q^{40} \) \(\mathstrut -\mathstrut 33524106q^{41} \) \(\mathstrut +\mathstrut 21373702q^{42} \) \(\mathstrut -\mathstrut 57566072q^{43} \) \(\mathstrut +\mathstrut 78361008q^{44} \) \(\mathstrut +\mathstrut 52112980q^{45} \) \(\mathstrut +\mathstrut 102115248q^{46} \) \(\mathstrut -\mathstrut 92563980q^{47} \) \(\mathstrut -\mathstrut 12007714q^{48} \) \(\mathstrut +\mathstrut 28824005q^{49} \) \(\mathstrut -\mathstrut 14987571q^{50} \) \(\mathstrut +\mathstrut 33824628q^{51} \) \(\mathstrut -\mathstrut 47441660q^{52} \) \(\mathstrut +\mathstrut 12312798q^{53} \) \(\mathstrut -\mathstrut 65044828q^{54} \) \(\mathstrut -\mathstrut 23377216q^{55} \) \(\mathstrut +\mathstrut 27465039q^{56} \) \(\mathstrut +\mathstrut 40252228q^{57} \) \(\mathstrut -\mathstrut 92605826q^{58} \) \(\mathstrut -\mathstrut 49659318q^{59} \) \(\mathstrut -\mathstrut 103385632q^{60} \) \(\mathstrut +\mathstrut 236063228q^{61} \) \(\mathstrut +\mathstrut 7926732q^{62} \) \(\mathstrut -\mathstrut 88930639q^{63} \) \(\mathstrut +\mathstrut 155269313q^{64} \) \(\mathstrut -\mathstrut 5696040q^{65} \) \(\mathstrut -\mathstrut 91316416q^{66} \) \(\mathstrut -\mathstrut 497097124q^{67} \) \(\mathstrut +\mathstrut 909131622q^{68} \) \(\mathstrut +\mathstrut 62722704q^{69} \) \(\mathstrut -\mathstrut 339126844q^{70} \) \(\mathstrut +\mathstrut 503008320q^{71} \) \(\mathstrut -\mathstrut 888461985q^{72} \) \(\mathstrut -\mathstrut 154939878q^{73} \) \(\mathstrut -\mathstrut 687124938q^{74} \) \(\mathstrut +\mathstrut 1092259130q^{75} \) \(\mathstrut +\mathstrut 1011351754q^{76} \) \(\mathstrut -\mathstrut 93062760q^{77} \) \(\mathstrut +\mathstrut 375103736q^{78} \) \(\mathstrut -\mathstrut 491877560q^{79} \) \(\mathstrut -\mathstrut 1083429216q^{80} \) \(\mathstrut -\mathstrut 621573311q^{81} \) \(\mathstrut +\mathstrut 952261394q^{82} \) \(\mathstrut -\mathstrut 656493222q^{83} \) \(\mathstrut -\mathstrut 380611322q^{84} \) \(\mathstrut +\mathstrut 611654472q^{85} \) \(\mathstrut -\mathstrut 1297812864q^{86} \) \(\mathstrut -\mathstrut 593687252q^{87} \) \(\mathstrut +\mathstrut 220113984q^{88} \) \(\mathstrut +\mathstrut 1143083874q^{89} \) \(\mathstrut +\mathstrut 2030209892q^{90} \) \(\mathstrut +\mathstrut 16201948q^{91} \) \(\mathstrut +\mathstrut 361692000q^{92} \) \(\mathstrut +\mathstrut 901734552q^{93} \) \(\mathstrut +\mathstrut 1235781636q^{94} \) \(\mathstrut -\mathstrut 1098323088q^{95} \) \(\mathstrut -\mathstrut 1381595390q^{96} \) \(\mathstrut -\mathstrut 2280214314q^{97} \) \(\mathstrut +\mathstrut 86472015q^{98} \) \(\mathstrut -\mathstrut 491561312q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(7))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7
7.10.a.a \(2\) \(3.605\) \(\Q(\sqrt{193}) \) None \(-6\) \(-86\) \(-2238\) \(-4802\) \(+\) \(q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots\)
7.10.a.b \(3\) \(3.605\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(21\) \(84\) \(1554\) \(7203\) \(-\) \(q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots\)