Properties

Label 17.4
Level 17
Weight 4
Dimension 28
Nonzero newspaces 4
Newforms 5
Sturm bound 96
Trace bound 3

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(17))\).

Total New Old
Modular forms 44 42 2
Cusp forms 28 28 0
Eisenstein series 16 14 2

Trace form

\(28q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 112q^{10} \) \(\mathstrut -\mathstrut 120q^{11} \) \(\mathstrut -\mathstrut 104q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut +\mathstrut 152q^{14} \) \(\mathstrut +\mathstrut 328q^{15} \) \(\mathstrut +\mathstrut 432q^{16} \) \(\mathstrut +\mathstrut 120q^{17} \) \(\mathstrut +\mathstrut 432q^{18} \) \(\mathstrut +\mathstrut 72q^{19} \) \(\mathstrut +\mathstrut 104q^{20} \) \(\mathstrut -\mathstrut 104q^{21} \) \(\mathstrut -\mathstrut 232q^{22} \) \(\mathstrut -\mathstrut 216q^{23} \) \(\mathstrut -\mathstrut 1880q^{24} \) \(\mathstrut -\mathstrut 1236q^{25} \) \(\mathstrut -\mathstrut 1040q^{26} \) \(\mathstrut -\mathstrut 224q^{27} \) \(\mathstrut +\mathstrut 136q^{28} \) \(\mathstrut +\mathstrut 252q^{29} \) \(\mathstrut +\mathstrut 1336q^{30} \) \(\mathstrut +\mathstrut 856q^{31} \) \(\mathstrut +\mathstrut 1168q^{32} \) \(\mathstrut +\mathstrut 1040q^{33} \) \(\mathstrut +\mathstrut 2104q^{34} \) \(\mathstrut +\mathstrut 976q^{35} \) \(\mathstrut +\mathstrut 1656q^{36} \) \(\mathstrut +\mathstrut 664q^{37} \) \(\mathstrut -\mathstrut 336q^{38} \) \(\mathstrut -\mathstrut 1224q^{39} \) \(\mathstrut -\mathstrut 2504q^{40} \) \(\mathstrut -\mathstrut 1428q^{41} \) \(\mathstrut -\mathstrut 2936q^{42} \) \(\mathstrut -\mathstrut 1472q^{43} \) \(\mathstrut -\mathstrut 1960q^{44} \) \(\mathstrut -\mathstrut 1348q^{45} \) \(\mathstrut -\mathstrut 1016q^{46} \) \(\mathstrut +\mathstrut 1512q^{47} \) \(\mathstrut +\mathstrut 3296q^{48} \) \(\mathstrut +\mathstrut 1528q^{49} \) \(\mathstrut +\mathstrut 2784q^{50} \) \(\mathstrut +\mathstrut 1592q^{51} \) \(\mathstrut +\mathstrut 3056q^{52} \) \(\mathstrut -\mathstrut 316q^{53} \) \(\mathstrut -\mathstrut 2696q^{54} \) \(\mathstrut -\mathstrut 1896q^{55} \) \(\mathstrut -\mathstrut 1008q^{56} \) \(\mathstrut -\mathstrut 2096q^{57} \) \(\mathstrut -\mathstrut 1488q^{58} \) \(\mathstrut -\mathstrut 872q^{59} \) \(\mathstrut -\mathstrut 1424q^{60} \) \(\mathstrut +\mathstrut 232q^{61} \) \(\mathstrut -\mathstrut 1872q^{62} \) \(\mathstrut +\mathstrut 1960q^{63} \) \(\mathstrut -\mathstrut 2104q^{64} \) \(\mathstrut +\mathstrut 1092q^{65} \) \(\mathstrut +\mathstrut 5168q^{66} \) \(\mathstrut +\mathstrut 2128q^{67} \) \(\mathstrut +\mathstrut 3632q^{68} \) \(\mathstrut +\mathstrut 3728q^{69} \) \(\mathstrut +\mathstrut 1264q^{70} \) \(\mathstrut +\mathstrut 184q^{71} \) \(\mathstrut +\mathstrut 48q^{72} \) \(\mathstrut +\mathstrut 292q^{73} \) \(\mathstrut +\mathstrut 256q^{74} \) \(\mathstrut +\mathstrut 856q^{75} \) \(\mathstrut +\mathstrut 480q^{76} \) \(\mathstrut -\mathstrut 216q^{77} \) \(\mathstrut -\mathstrut 1792q^{78} \) \(\mathstrut -\mathstrut 360q^{79} \) \(\mathstrut -\mathstrut 872q^{80} \) \(\mathstrut -\mathstrut 2992q^{81} \) \(\mathstrut -\mathstrut 424q^{82} \) \(\mathstrut -\mathstrut 5504q^{83} \) \(\mathstrut -\mathstrut 8352q^{84} \) \(\mathstrut -\mathstrut 4316q^{85} \) \(\mathstrut -\mathstrut 8512q^{86} \) \(\mathstrut -\mathstrut 1496q^{87} \) \(\mathstrut +\mathstrut 1720q^{88} \) \(\mathstrut -\mathstrut 1112q^{89} \) \(\mathstrut -\mathstrut 1056q^{90} \) \(\mathstrut +\mathstrut 1432q^{91} \) \(\mathstrut +\mathstrut 3464q^{92} \) \(\mathstrut +\mathstrut 2232q^{93} \) \(\mathstrut +\mathstrut 3928q^{94} \) \(\mathstrut +\mathstrut 3880q^{95} \) \(\mathstrut +\mathstrut 5984q^{96} \) \(\mathstrut +\mathstrut 280q^{97} \) \(\mathstrut +\mathstrut 8568q^{98} \) \(\mathstrut -\mathstrut 2616q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
17.4.a \(\chi_{17}(1, \cdot)\) 17.4.a.a 1 1
17.4.a.b 3
17.4.b \(\chi_{17}(16, \cdot)\) 17.4.b.a 4 1
17.4.c \(\chi_{17}(4, \cdot)\) 17.4.c.a 8 2
17.4.d \(\chi_{17}(2, \cdot)\) 17.4.d.a 12 4