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Properties

Label 59.5
Level 59
Weight 5
Dimension 551
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 1450
Trace bound 1

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(1450\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(59))\).

Total New Old
Modular forms 609 609 0
Cusp forms 551 551 0
Eisenstein series 58 58 0

Trace form

\( 551 q - 29 q^{2} - 29 q^{3} - 29 q^{4} - 29 q^{5} - 29 q^{6} - 29 q^{7} - 29 q^{8} - 29 q^{9} + O(q^{10}) \) \( 551 q - 29 q^{2} - 29 q^{3} - 29 q^{4} - 29 q^{5} - 29 q^{6} - 29 q^{7} - 29 q^{8} - 29 q^{9} - 29 q^{10} - 29 q^{11} - 29 q^{12} - 29 q^{13} - 29 q^{14} - 29 q^{15} - 29 q^{16} - 29 q^{17} - 29 q^{18} - 29 q^{19} - 29 q^{20} - 29 q^{21} - 29 q^{22} - 29 q^{23} - 29 q^{24} - 29 q^{25} - 29 q^{26} - 29 q^{27} - 29 q^{28} - 29 q^{29} - 29 q^{30} - 29 q^{31} - 29 q^{32} - 29 q^{33} - 29 q^{34} - 29 q^{35} - 29 q^{36} - 29 q^{37} - 29 q^{38} - 29 q^{39} - 29 q^{40} - 29 q^{41} - 29 q^{42} - 29 q^{43} - 29 q^{44} + 29754 q^{45} + 36163 q^{46} + 8584 q^{47} + 6931 q^{48} - 8903 q^{49} - 33437 q^{50} - 43065 q^{51} - 47357 q^{52} - 23519 q^{53} - 74733 q^{54} - 26390 q^{55} - 50141 q^{56} - 16414 q^{57} + 6757 q^{59} + 80678 q^{60} + 19633 q^{61} + 25027 q^{62} + 73196 q^{63} + 128035 q^{64} + 49300 q^{65} + 110403 q^{66} + 27637 q^{67} + 41731 q^{68} + 21663 q^{69} - 5597 q^{70} - 20387 q^{71} - 126701 q^{72} - 34394 q^{73} - 100253 q^{74} - 68556 q^{75} - 29 q^{76} - 29 q^{77} - 29 q^{78} - 29 q^{79} - 29 q^{80} - 29 q^{81} - 29 q^{82} - 29 q^{83} - 29 q^{84} - 29 q^{85} - 29 q^{86} - 29 q^{87} - 29 q^{88} - 29 q^{89} - 29 q^{90} - 29 q^{91} - 29 q^{92} - 29 q^{93} - 29 q^{94} - 29 q^{95} - 29 q^{96} - 29 q^{97} + 272716 q^{98} + 197287 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(59))\)

We only show spaces with odd 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
59.5.b \(\chi_{59}(58, \cdot)\) 59.5.b.a 3 1
59.5.b.b 16
59.5.d \(\chi_{59}(2, \cdot)\) 59.5.d.a 532 28