Properties

Label 89.2
Level 89
Weight 2
Dimension 287
Nonzero newspaces 6
Newforms 8
Sturm bound 1320
Trace bound 2

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Defining parameters

Level: \( N \) = \( 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 8 \)
Sturm bound: \(1320\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(89))\).

Total New Old
Modular forms 374 374 0
Cusp forms 287 287 0
Eisenstein series 87 87 0

Trace form

\( 287q - 41q^{2} - 40q^{3} - 37q^{4} - 38q^{5} - 32q^{6} - 36q^{7} - 29q^{8} - 31q^{9} + O(q^{10}) \) \( 287q - 41q^{2} - 40q^{3} - 37q^{4} - 38q^{5} - 32q^{6} - 36q^{7} - 29q^{8} - 31q^{9} - 26q^{10} - 32q^{11} - 16q^{12} - 30q^{13} - 20q^{14} - 20q^{15} - 13q^{16} - 26q^{17} - 5q^{18} - 24q^{19} - 2q^{20} - 12q^{21} - 8q^{22} - 20q^{23} + 16q^{24} - 13q^{25} - 2q^{26} - 4q^{27} + 12q^{28} - 14q^{29} + 28q^{30} - 12q^{31} + 19q^{32} + 4q^{33} + 10q^{34} + 4q^{35} + 47q^{36} - 6q^{37} + 16q^{38} + 12q^{39} + 46q^{40} - 2q^{41} + 52q^{42} + 40q^{44} + 34q^{45} + 28q^{46} + 4q^{47} + 80q^{48} + 13q^{49} + 49q^{50} + 28q^{51} + 54q^{52} + 10q^{53} + 76q^{54} + 28q^{55} + 76q^{56} + 36q^{57} + 46q^{58} + 16q^{59} + 124q^{60} + 18q^{61} + 52q^{62} + 60q^{63} + 83q^{64} + 40q^{65} + 100q^{66} + 24q^{67} + 82q^{68} + 52q^{69} + 100q^{70} + 28q^{71} + 19q^{72} - 14q^{73} - 40q^{74} - 140q^{75} - 168q^{76} - 36q^{77} - 140q^{78} - 52q^{79} - 188q^{80} - 143q^{81} - 94q^{82} - 92q^{83} - 436q^{84} - 68q^{85} - 88q^{86} - 144q^{87} - 172q^{88} - 131q^{89} - 382q^{90} - 108q^{91} - 140q^{92} - 136q^{93} - 76q^{94} - 56q^{95} - 408q^{96} - 78q^{97} - 49q^{98} - 108q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)

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
89.2.a \(\chi_{89}(1, \cdot)\) 89.2.a.a 1 1
89.2.a.b 1
89.2.a.c 5
89.2.b \(\chi_{89}(88, \cdot)\) 89.2.b.a 6 1
89.2.c \(\chi_{89}(34, \cdot)\) 89.2.c.a 14 2
89.2.e \(\chi_{89}(2, \cdot)\) 89.2.e.a 60 10
89.2.f \(\chi_{89}(11, \cdot)\) 89.2.f.a 60 10
89.2.g \(\chi_{89}(5, \cdot)\) 89.2.g.a 140 20