Properties

Label 289.2
Level 289
Weight 2
Dimension 3259
Nonzero newspaces 8
Newform subspaces 24
Sturm bound 13872
Trace bound 2

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Defining parameters

Level: \( N \) = \( 289 = 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 24 \)
Sturm bound: \(13872\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(289))\).

Total New Old
Modular forms 3668 3628 40
Cusp forms 3269 3259 10
Eisenstein series 399 369 30

Trace form

\( 3259q - 123q^{2} - 124q^{3} - 127q^{4} - 126q^{5} - 132q^{6} - 128q^{7} - 135q^{8} - 133q^{9} + O(q^{10}) \) \( 3259q - 123q^{2} - 124q^{3} - 127q^{4} - 126q^{5} - 132q^{6} - 128q^{7} - 135q^{8} - 133q^{9} - 130q^{10} - 116q^{11} - 100q^{12} - 118q^{13} - 112q^{14} - 96q^{15} - 79q^{16} - 120q^{17} - 207q^{18} - 124q^{19} - 106q^{20} - 104q^{21} - 124q^{22} - 128q^{23} - 100q^{24} - 95q^{25} - 90q^{26} - 112q^{27} - 80q^{28} - 110q^{29} - 64q^{30} - 88q^{31} - 71q^{32} - 88q^{33} - 64q^{34} - 216q^{35} - 51q^{36} - 94q^{37} - 84q^{38} - 80q^{39} - 18q^{40} - 74q^{41} - 24q^{42} - 84q^{43} - 12q^{44} - 94q^{45} - 96q^{46} - 88q^{47} - 36q^{48} - 113q^{49} - 85q^{50} - 96q^{51} - 202q^{52} - 86q^{53} - 64q^{55} - 8q^{57} - 34q^{58} - 52q^{59} + 48q^{60} - 54q^{61} - 8q^{62} + 16q^{63} - 23q^{64} - 52q^{65} - 8q^{66} - 108q^{67} - 28q^{68} - 104q^{69} + 8q^{70} - 96q^{71} + 77q^{72} + 6q^{73} - 66q^{74} + 12q^{75} - 20q^{76} - 56q^{77} + 48q^{78} - 72q^{79} + 46q^{80} - 33q^{81} - 30q^{82} - 76q^{83} + 24q^{84} - 36q^{85} - 140q^{86} - 48q^{87} + 20q^{88} - 66q^{89} + 102q^{90} - 8q^{91} + 96q^{92} - 56q^{93} + 56q^{94} - 16q^{95} + 156q^{96} - 90q^{97} + 53q^{98} + 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)

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
289.2.a \(\chi_{289}(1, \cdot)\) 289.2.a.a 1 1
289.2.a.b 2
289.2.a.c 2
289.2.a.d 3
289.2.a.e 3
289.2.a.f 4
289.2.b \(\chi_{289}(288, \cdot)\) 289.2.b.a 2 1
289.2.b.b 4
289.2.b.c 4
289.2.b.d 6
289.2.c \(\chi_{289}(38, \cdot)\) 289.2.c.a 4 2
289.2.c.b 8
289.2.c.c 8
289.2.c.d 12
289.2.d \(\chi_{289}(110, \cdot)\) 289.2.d.a 4 4
289.2.d.b 4
289.2.d.c 4
289.2.d.d 8
289.2.d.e 16
289.2.d.f 24
289.2.f \(\chi_{289}(18, \cdot)\) 289.2.f.a 384 16
289.2.g \(\chi_{289}(16, \cdot)\) 289.2.g.a 384 16
289.2.h \(\chi_{289}(4, \cdot)\) 289.2.h.a 768 32
289.2.i \(\chi_{289}(2, \cdot)\) 289.2.i.a 1600 64

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(289))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(289)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)