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

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

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 \(1\) \(4\) \(-8\) \(22\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)