Properties

Label 289.4
Level 289
Weight 4
Dimension 10148
Nonzero newspaces 8
Sturm bound 27744
Trace bound 3

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Defining parameters

Level: \( N \) = \( 289 = 17^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(27744\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(289))\).

Total New Old
Modular forms 10604 10517 87
Cusp forms 10204 10148 56
Eisenstein series 400 369 31

Trace form

\( 10148 q - 120 q^{2} - 120 q^{3} - 120 q^{4} - 120 q^{5} - 120 q^{6} - 120 q^{7} - 120 q^{8} - 120 q^{9} + O(q^{10}) \) \( 10148 q - 120 q^{2} - 120 q^{3} - 120 q^{4} - 120 q^{5} - 120 q^{6} - 120 q^{7} - 120 q^{8} - 120 q^{9} + 88 q^{10} + 104 q^{11} + 72 q^{12} - 184 q^{13} - 440 q^{14} - 792 q^{15} - 1000 q^{16} - 256 q^{17} - 1128 q^{18} - 280 q^{19} - 344 q^{20} + 72 q^{21} + 328 q^{22} + 296 q^{23} + 3624 q^{24} + 2336 q^{25} + 1944 q^{26} + 312 q^{27} - 408 q^{28} - 640 q^{29} - 2808 q^{30} - 1848 q^{31} - 2472 q^{32} - 2216 q^{33} - 2240 q^{34} - 2216 q^{35} - 3448 q^{36} - 1464 q^{37} + 536 q^{38} + 2312 q^{39} + 4872 q^{40} + 2720 q^{41} + 5736 q^{42} + 2808 q^{43} + 3784 q^{44} + 2560 q^{45} + 1896 q^{46} - 3160 q^{47} - 6728 q^{48} - 3192 q^{49} - 5704 q^{50} - 1728 q^{51} - 6376 q^{52} + 496 q^{53} + 5256 q^{54} + 3656 q^{55} + 1880 q^{56} + 4056 q^{57} + 2840 q^{58} + 1608 q^{59} + 2712 q^{60} - 600 q^{61} + 3608 q^{62} - 4056 q^{63} + 4072 q^{64} - 2320 q^{65} - 10472 q^{66} - 4392 q^{67} - 3768 q^{68} - 7720 q^{69} - 2664 q^{70} - 504 q^{71} - 232 q^{72} - 720 q^{73} - 648 q^{74} - 1848 q^{75} - 1096 q^{76} + 296 q^{77} + 3448 q^{78} + 584 q^{79} + 1608 q^{80} + 5848 q^{81} + 712 q^{82} + 10872 q^{83} + 16568 q^{84} + 4180 q^{85} + 16760 q^{86} + 2856 q^{87} - 3576 q^{88} + 2088 q^{89} + 1976 q^{90} - 3000 q^{91} - 7064 q^{92} - 4600 q^{93} - 7992 q^{94} - 7896 q^{95} - 12104 q^{96} - 696 q^{97} - 17272 q^{98} + 5096 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)

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
289.4.a \(\chi_{289}(1, \cdot)\) 289.4.a.a 1 1
289.4.a.b 3
289.4.a.c 4
289.4.a.d 4
289.4.a.e 4
289.4.a.f 8
289.4.a.g 12
289.4.a.h 12
289.4.a.i 12
289.4.b \(\chi_{289}(288, \cdot)\) 289.4.b.a 2 1
289.4.b.b 6
289.4.b.c 8
289.4.b.d 8
289.4.b.e 12
289.4.b.f 24
289.4.c \(\chi_{289}(38, \cdot)\) n/a 120 2
289.4.d \(\chi_{289}(110, \cdot)\) n/a 244 4
289.4.f \(\chi_{289}(18, \cdot)\) n/a 1216 16
289.4.g \(\chi_{289}(16, \cdot)\) n/a 1216 16
289.4.h \(\chi_{289}(4, \cdot)\) n/a 2432 32
289.4.i \(\chi_{289}(2, \cdot)\) n/a 4800 64

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(289))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(289)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)