Properties

Label 17.10.a
Level 17
Weight 10
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 2
Sturm bound 15
Trace bound 1

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 17.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(15\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(17))\).

Total New Old
Modular forms 14 12 2
Cusp forms 12 12 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.

\(17\)Dim.
\(+\)\(5\)
\(-\)\(7\)

Trace form

\(12q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 148q^{3} \) \(\mathstrut +\mathstrut 3242q^{4} \) \(\mathstrut +\mathstrut 2842q^{5} \) \(\mathstrut -\mathstrut 4142q^{6} \) \(\mathstrut -\mathstrut 3814q^{7} \) \(\mathstrut -\mathstrut 25602q^{8} \) \(\mathstrut +\mathstrut 92400q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 148q^{3} \) \(\mathstrut +\mathstrut 3242q^{4} \) \(\mathstrut +\mathstrut 2842q^{5} \) \(\mathstrut -\mathstrut 4142q^{6} \) \(\mathstrut -\mathstrut 3814q^{7} \) \(\mathstrut -\mathstrut 25602q^{8} \) \(\mathstrut +\mathstrut 92400q^{9} \) \(\mathstrut +\mathstrut 64898q^{10} \) \(\mathstrut +\mathstrut 67500q^{11} \) \(\mathstrut -\mathstrut 207850q^{12} \) \(\mathstrut +\mathstrut 7260q^{13} \) \(\mathstrut +\mathstrut 362552q^{14} \) \(\mathstrut -\mathstrut 528276q^{15} \) \(\mathstrut +\mathstrut 1813810q^{16} \) \(\mathstrut +\mathstrut 167042q^{17} \) \(\mathstrut -\mathstrut 1762558q^{18} \) \(\mathstrut +\mathstrut 406180q^{19} \) \(\mathstrut +\mathstrut 715478q^{20} \) \(\mathstrut -\mathstrut 1628224q^{21} \) \(\mathstrut -\mathstrut 1100230q^{22} \) \(\mathstrut +\mathstrut 3003634q^{23} \) \(\mathstrut +\mathstrut 1191342q^{24} \) \(\mathstrut +\mathstrut 4336024q^{25} \) \(\mathstrut -\mathstrut 13645120q^{26} \) \(\mathstrut -\mathstrut 7517332q^{27} \) \(\mathstrut -\mathstrut 3145520q^{28} \) \(\mathstrut +\mathstrut 4635618q^{29} \) \(\mathstrut +\mathstrut 4489552q^{30} \) \(\mathstrut -\mathstrut 3715622q^{31} \) \(\mathstrut -\mathstrut 780458q^{32} \) \(\mathstrut +\mathstrut 593116q^{33} \) \(\mathstrut +\mathstrut 2672672q^{34} \) \(\mathstrut -\mathstrut 27034724q^{35} \) \(\mathstrut +\mathstrut 54317142q^{36} \) \(\mathstrut -\mathstrut 13124210q^{37} \) \(\mathstrut -\mathstrut 30849320q^{38} \) \(\mathstrut +\mathstrut 43856988q^{39} \) \(\mathstrut +\mathstrut 73224598q^{40} \) \(\mathstrut +\mathstrut 2288748q^{41} \) \(\mathstrut -\mathstrut 29899080q^{42} \) \(\mathstrut -\mathstrut 34995064q^{43} \) \(\mathstrut +\mathstrut 140019678q^{44} \) \(\mathstrut +\mathstrut 121715946q^{45} \) \(\mathstrut -\mathstrut 183572956q^{46} \) \(\mathstrut +\mathstrut 39736464q^{47} \) \(\mathstrut -\mathstrut 304192994q^{48} \) \(\mathstrut +\mathstrut 15226292q^{49} \) \(\mathstrut -\mathstrut 175229210q^{50} \) \(\mathstrut +\mathstrut 27060804q^{51} \) \(\mathstrut +\mathstrut 17392704q^{52} \) \(\mathstrut +\mathstrut 38450580q^{53} \) \(\mathstrut +\mathstrut 292953820q^{54} \) \(\mathstrut +\mathstrut 47156492q^{55} \) \(\mathstrut +\mathstrut 121233936q^{56} \) \(\mathstrut +\mathstrut 290228864q^{57} \) \(\mathstrut -\mathstrut 172256422q^{58} \) \(\mathstrut -\mathstrut 8724216q^{59} \) \(\mathstrut -\mathstrut 851802400q^{60} \) \(\mathstrut -\mathstrut 127601298q^{61} \) \(\mathstrut +\mathstrut 251348744q^{62} \) \(\mathstrut -\mathstrut 194130634q^{63} \) \(\mathstrut +\mathstrut 449545162q^{64} \) \(\mathstrut -\mathstrut 162954956q^{65} \) \(\mathstrut -\mathstrut 326848468q^{66} \) \(\mathstrut -\mathstrut 2640180q^{67} \) \(\mathstrut +\mathstrut 128288256q^{68} \) \(\mathstrut +\mathstrut 46274160q^{69} \) \(\mathstrut +\mathstrut 843528568q^{70} \) \(\mathstrut +\mathstrut 175871018q^{71} \) \(\mathstrut -\mathstrut 645941526q^{72} \) \(\mathstrut +\mathstrut 16675856q^{73} \) \(\mathstrut +\mathstrut 511462886q^{74} \) \(\mathstrut +\mathstrut 765386140q^{75} \) \(\mathstrut -\mathstrut 902581384q^{76} \) \(\mathstrut -\mathstrut 245828184q^{77} \) \(\mathstrut +\mathstrut 1015080612q^{78} \) \(\mathstrut +\mathstrut 130907274q^{79} \) \(\mathstrut +\mathstrut 220577342q^{80} \) \(\mathstrut +\mathstrut 516841632q^{81} \) \(\mathstrut -\mathstrut 63174400q^{82} \) \(\mathstrut -\mathstrut 1318264120q^{83} \) \(\mathstrut +\mathstrut 1059929000q^{84} \) \(\mathstrut -\mathstrut 9855478q^{85} \) \(\mathstrut +\mathstrut 999753908q^{86} \) \(\mathstrut -\mathstrut 1454400972q^{87} \) \(\mathstrut +\mathstrut 114058870q^{88} \) \(\mathstrut -\mathstrut 1594479008q^{89} \) \(\mathstrut -\mathstrut 4524752134q^{90} \) \(\mathstrut -\mathstrut 866519200q^{91} \) \(\mathstrut +\mathstrut 3407899844q^{92} \) \(\mathstrut +\mathstrut 2696236984q^{93} \) \(\mathstrut +\mathstrut 290020128q^{94} \) \(\mathstrut -\mathstrut 1750951648q^{95} \) \(\mathstrut -\mathstrut 1506989058q^{96} \) \(\mathstrut +\mathstrut 2698561500q^{97} \) \(\mathstrut -\mathstrut 1298895954q^{98} \) \(\mathstrut -\mathstrut 552052864q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(17))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.10.a.a \(5\) \(8.756\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-33\) \(-236\) \(1480\) \(-13202\) \(+\) \(q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots\)
17.10.a.b \(7\) \(8.756\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(88\) \(1362\) \(9388\) \(-\) \(q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)