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Properties

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

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Defining parameters

Level: \( N \) = \( 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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