Properties

Label 43.3
Level 43
Weight 3
Dimension 133
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 462
Trace bound 1

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Defining parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(462\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(43))\).

Total New Old
Modular forms 175 175 0
Cusp forms 133 133 0
Eisenstein series 42 42 0

Trace form

\( 133 q - 21 q^{2} - 21 q^{3} - 21 q^{4} - 21 q^{5} - 21 q^{6} - 21 q^{7} - 21 q^{8} - 21 q^{9} + O(q^{10}) \) \( 133 q - 21 q^{2} - 21 q^{3} - 21 q^{4} - 21 q^{5} - 21 q^{6} - 21 q^{7} - 21 q^{8} - 21 q^{9} - 21 q^{10} - 21 q^{11} - 21 q^{12} - 21 q^{13} - 21 q^{14} - 21 q^{15} - 21 q^{16} - 21 q^{17} - 21 q^{18} - 21 q^{19} - 21 q^{20} - 21 q^{21} - 21 q^{22} - 21 q^{23} - 21 q^{24} - 21 q^{25} - 21 q^{26} - 21 q^{27} - 21 q^{28} - 21 q^{29} - 21 q^{30} + 56 q^{31} + 399 q^{32} + 357 q^{33} + 483 q^{34} + 273 q^{35} + 651 q^{36} + 189 q^{37} + 315 q^{38} + 126 q^{39} + 315 q^{40} - 126 q^{43} - 210 q^{44} - 336 q^{45} - 357 q^{46} - 126 q^{47} - 1029 q^{48} - 364 q^{49} - 693 q^{50} - 399 q^{51} - 1141 q^{52} - 483 q^{53} - 777 q^{54} - 567 q^{55} - 609 q^{56} - 126 q^{57} - 21 q^{58} - 21 q^{59} - 21 q^{60} - 21 q^{61} - 21 q^{62} - 21 q^{63} - 21 q^{64} - 21 q^{65} - 21 q^{66} - 21 q^{67} - 21 q^{68} + 651 q^{69} + 1239 q^{70} + 567 q^{71} + 2709 q^{72} + 483 q^{73} + 1596 q^{74} + 1449 q^{75} + 1302 q^{76} + 987 q^{77} + 1890 q^{78} + 483 q^{79} + 819 q^{80} + 651 q^{81} + 609 q^{82} + 147 q^{83} + 441 q^{84} - 189 q^{86} - 462 q^{87} - 609 q^{88} - 357 q^{89} - 1911 q^{90} - 525 q^{91} - 1491 q^{92} - 1365 q^{93} - 1533 q^{94} - 861 q^{95} - 3024 q^{96} - 1533 q^{97} - 1932 q^{98} - 2079 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(43))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
43.3.b \(\chi_{43}(42, \cdot)\) 43.3.b.a 1 1
43.3.b.b 6
43.3.d \(\chi_{43}(7, \cdot)\) 43.3.d.a 12 2
43.3.f \(\chi_{43}(2, \cdot)\) 43.3.f.a 42 6
43.3.h \(\chi_{43}(3, \cdot)\) 43.3.h.a 72 12