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Properties

Label 59.7
Level 59
Weight 7
Dimension 841
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 2030
Trace bound 1

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(2030\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(59))\).

Total New Old
Modular forms 899 899 0
Cusp forms 841 841 0
Eisenstein series 58 58 0

Trace form

\( 841 q - 29 q^{2} - 29 q^{3} - 29 q^{4} - 29 q^{5} - 29 q^{6} - 29 q^{7} - 29 q^{8} - 29 q^{9} + O(q^{10}) \) \( 841 q - 29 q^{2} - 29 q^{3} - 29 q^{4} - 29 q^{5} - 29 q^{6} - 29 q^{7} - 29 q^{8} - 29 q^{9} - 29 q^{10} - 29 q^{11} - 29 q^{12} - 29 q^{13} - 29 q^{14} - 29 q^{15} - 29 q^{16} - 29 q^{17} - 29 q^{18} - 29 q^{19} - 29 q^{20} - 29 q^{21} - 29 q^{22} - 29 q^{23} - 29 q^{24} - 29 q^{25} - 29 q^{26} - 29 q^{27} - 29 q^{28} - 29 q^{29} - 29 q^{30} - 29 q^{31} - 29 q^{32} - 29 q^{33} - 29 q^{34} - 29 q^{35} - 29 q^{36} - 29 q^{37} - 29 q^{38} - 29 q^{39} - 29 q^{40} - 29 q^{41} - 29 q^{42} - 29 q^{43} - 29 q^{44} + 1589403 q^{45} + 409219 q^{46} - 472149 q^{47} - 3981149 q^{48} - 1102493 q^{49} - 1117341 q^{50} + 168867 q^{51} + 1336291 q^{52} + 1088051 q^{53} + 4504947 q^{54} + 1872907 q^{55} + 3956963 q^{56} + 1380371 q^{57} - 592093 q^{59} - 6859834 q^{60} - 1574381 q^{61} - 1814269 q^{62} - 4518229 q^{63} - 6080285 q^{64} - 1422653 q^{65} - 435261 q^{66} + 876931 q^{67} + 3860451 q^{68} + 5706243 q^{69} + 6798499 q^{70} + 3251219 q^{71} + 6041251 q^{72} - 396749 q^{73} - 5742493 q^{74} - 6752157 q^{75} - 29 q^{76} - 29 q^{77} - 29 q^{78} - 29 q^{79} - 29 q^{80} - 29 q^{81} - 29 q^{82} - 29 q^{83} - 29 q^{84} - 29 q^{85} - 29 q^{86} - 29 q^{87} - 29 q^{88} - 29 q^{89} - 29 q^{90} - 29 q^{91} - 29 q^{92} - 29 q^{93} - 29 q^{94} - 29 q^{95} - 29 q^{96} - 29 q^{97} + 29127484 q^{98} + 9513421 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(59))\)

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
59.7.b \(\chi_{59}(58, \cdot)\) 59.7.b.a 1 1
59.7.b.b 2
59.7.b.c 26
59.7.d \(\chi_{59}(2, \cdot)\) 59.7.d.a 812 28