Properties

Label 17.4.a
Level 17
Weight 4
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 17.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 \(M_{4}(\Gamma_0(17))\).

Total New Old
Modular forms 6 4 2
Cusp forms 4 4 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.
\(+\)\(3\)
\(-\)\(1\)

Trace form

\( 4q - 2q^{2} - 4q^{3} + 26q^{4} - 2q^{5} - 50q^{6} - 6q^{7} - 18q^{8} + 96q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 4q^{3} + 26q^{4} - 2q^{5} - 50q^{6} - 6q^{7} - 18q^{8} + 96q^{9} - 74q^{10} - 52q^{11} + 14q^{12} - 28q^{13} + 176q^{14} + 60q^{15} + 66q^{16} - 34q^{17} - 214q^{18} + 196q^{19} - 162q^{20} + 32q^{21} + 358q^{22} + 82q^{23} - 834q^{24} - 312q^{25} + 200q^{26} - 100q^{27} + 448q^{28} - 426q^{29} + 544q^{30} + 58q^{31} - 26q^{32} - 140q^{33} - 68q^{34} - 500q^{35} + 1350q^{36} + 298q^{37} + 376q^{38} + 732q^{39} - 298q^{40} - 636q^{41} - 1800q^{42} + 408q^{43} - 1146q^{44} - 162q^{45} - 524q^{46} + 928q^{47} + 1342q^{48} + 172q^{49} + 814q^{50} - 204q^{51} - 832q^{52} + 620q^{53} - 860q^{54} - 68q^{55} + 96q^{56} - 1648q^{57} - 1394q^{58} + 888q^{59} + 1280q^{60} + 26q^{61} + 1024q^{62} + 86q^{63} - 486q^{64} + 60q^{65} + 1892q^{66} + 524q^{67} - 408q^{68} + 1056q^{69} - 1000q^{70} - 1110q^{71} - 150q^{72} + 1200q^{73} + 1010q^{74} - 836q^{75} - 792q^{76} + 168q^{77} - 84q^{78} - 1078q^{79} - 466q^{80} - 864q^{81} + 1384q^{82} - 1640q^{83} - 1816q^{84} + 238q^{85} - 820q^{86} + 1188q^{87} + 1334q^{88} - 944q^{89} - 2674q^{90} + 608q^{91} + 4836q^{92} + 2008q^{93} - 2880q^{94} + 224q^{95} + 318q^{96} - 652q^{97} + 1534q^{98} - 3808q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.4.a.a \(1\) \(1.003\) \(\Q\) None \(-3\) \(-8\) \(6\) \(-28\) \(-\) \(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b \(3\) \(1.003\) 3.3.2636.1 None \(1\) \(4\) \(-8\) \(22\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)