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Properties

Label 59.8
Level 59
Weight 8
Dimension 986
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 2320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(2320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(59))\).

Total New Old
Modular forms 1044 1042 2
Cusp forms 986 986 0
Eisenstein series 58 56 2

Trace form

\( 986 q - 29 q^{2} - 29 q^{3} - 29 q^{4} - 29 q^{5} - 29 q^{6} - 29 q^{7} - 29 q^{8} - 29 q^{9} + O(q^{10}) \) \( 986 q - 29 q^{2} - 29 q^{3} - 29 q^{4} - 29 q^{5} - 29 q^{6} - 29 q^{7} - 29 q^{8} - 29 q^{9} - 29 q^{10} - 29 q^{11} - 29 q^{12} - 29 q^{13} - 29 q^{14} - 29 q^{15} - 29 q^{16} - 29 q^{17} - 29 q^{18} - 29 q^{19} - 29 q^{20} - 29 q^{21} - 29 q^{22} - 29 q^{23} - 29 q^{24} - 29 q^{25} - 29 q^{26} - 29 q^{27} - 29 q^{28} - 29 q^{29} - 29 q^{30} - 29 q^{31} - 29 q^{32} - 29 q^{33} - 29 q^{34} - 29 q^{35} - 29 q^{36} - 29 q^{37} - 29 q^{38} - 29 q^{39} - 29 q^{40} - 29 q^{41} - 29 q^{42} - 29 q^{43} - 29 q^{44} - 10521490 q^{45} + 3039635 q^{46} + 4905698 q^{47} + 22305379 q^{48} + 1552457 q^{49} - 8484733 q^{50} - 15942721 q^{51} - 17765661 q^{52} - 7103463 q^{53} - 11661973 q^{54} + 2137648 q^{55} + 24306147 q^{56} + 24067506 q^{57} + 11316438 q^{58} + 10717617 q^{59} + 46748870 q^{60} + 2901305 q^{61} - 3215085 q^{62} - 23787714 q^{63} - 59050525 q^{64} - 26521892 q^{65} - 60021445 q^{66} - 12435055 q^{67} - 6956317 q^{68} + 17586383 q^{69} + 44197827 q^{70} + 32403585 q^{71} + 100413283 q^{72} + 8188614 q^{73} - 31018893 q^{74} - 62323030 q^{75} - 29 q^{76} - 29 q^{77} - 29 q^{78} - 29 q^{79} - 29 q^{80} - 29 q^{81} - 29 q^{82} - 29 q^{83} - 29 q^{84} - 29 q^{85} - 29 q^{86} - 29 q^{87} - 29 q^{88} - 29 q^{89} - 29 q^{90} - 29 q^{91} - 29 q^{92} - 29 q^{93} - 29 q^{94} - 29 q^{95} - 29 q^{96} - 29 q^{97} - 265320710 q^{98} - 11479592 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(59))\)

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
59.8.a \(\chi_{59}(1, \cdot)\) 59.8.a.a 14 1
59.8.a.b 20
59.8.c \(\chi_{59}(3, \cdot)\) 59.8.c.a 952 28