Properties

Label 43.2
Level 43
Weight 2
Dimension 57
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 308
Trace bound 1

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Defining parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(308\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(43))\).

Total New Old
Modular forms 98 98 0
Cusp forms 57 57 0
Eisenstein series 41 41 0

Trace form

\( 57 q - 18 q^{2} - 17 q^{3} - 14 q^{4} - 15 q^{5} - 9 q^{6} - 13 q^{7} - 6 q^{8} - 8 q^{9} + O(q^{10}) \) \( 57 q - 18 q^{2} - 17 q^{3} - 14 q^{4} - 15 q^{5} - 9 q^{6} - 13 q^{7} - 6 q^{8} - 8 q^{9} - 3 q^{10} - 9 q^{11} + 7 q^{12} - 7 q^{13} + 3 q^{14} + 3 q^{15} + 10 q^{16} - 3 q^{17} + 18 q^{18} - q^{19} + 21 q^{20} + 11 q^{21} + 15 q^{22} + 3 q^{23} + 39 q^{24} + 10 q^{25} + 21 q^{26} + 19 q^{27} + 35 q^{28} + 9 q^{29} + 51 q^{30} + 4 q^{31} - 15 q^{33} - 30 q^{34} - 15 q^{35} - 42 q^{36} - 25 q^{37} - 45 q^{38} - 14 q^{39} - 99 q^{40} - 30 q^{42} - 83 q^{43} - 42 q^{44} - 48 q^{45} - 33 q^{46} + 6 q^{47} - 65 q^{48} - 13 q^{49} - 12 q^{50} + 9 q^{51} - 35 q^{52} - 9 q^{53} + 36 q^{54} + 9 q^{55} + 57 q^{56} + 52 q^{57} + 69 q^{58} + 39 q^{59} + 147 q^{60} + 41 q^{61} + 75 q^{62} + 83 q^{63} + 106 q^{64} + 63 q^{65} + 123 q^{66} + 47 q^{67} + 105 q^{68} + 33 q^{69} + 39 q^{70} + 9 q^{71} - 36 q^{72} + 11 q^{73} - 54 q^{74} - 44 q^{75} - 28 q^{76} - 51 q^{77} - 126 q^{78} - 25 q^{79} - 3 q^{80} - 68 q^{81} - 105 q^{82} - 21 q^{83} - 217 q^{84} - 18 q^{85} - 60 q^{86} - 132 q^{87} - 51 q^{88} - 15 q^{89} - 165 q^{90} + 7 q^{91} - 63 q^{92} - 61 q^{93} - 45 q^{94} + 15 q^{95} - 42 q^{96} - 49 q^{97} + 3 q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
43.2.a \(\chi_{43}(1, \cdot)\) 43.2.a.a 1 1
43.2.a.b 2
43.2.c \(\chi_{43}(6, \cdot)\) 43.2.c.a 2 2
43.2.c.b 4
43.2.e \(\chi_{43}(4, \cdot)\) 43.2.e.a 6 6
43.2.e.b 6
43.2.g \(\chi_{43}(9, \cdot)\) 43.2.g.a 36 12