Properties

Label 43.5
Level 43
Weight 5
Dimension 287
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 770
Trace bound 1

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Defining parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(770\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(43))\).

Total New Old
Modular forms 329 329 0
Cusp forms 287 287 0
Eisenstein series 42 42 0

Trace form

\( 287q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10}) \) \( 287q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} + 4522q^{31} + 15099q^{32} + 5649q^{33} - 2037q^{34} - 6195q^{35} - 24213q^{36} - 10311q^{37} - 20181q^{38} - 10164q^{39} - 25557q^{40} - 1722q^{41} + 8904q^{43} + 14070q^{44} + 25494q^{45} + 25515q^{46} + 7224q^{47} + 60459q^{48} + 16786q^{49} + 24171q^{50} + 7917q^{51} + 4459q^{52} - 6951q^{53} - 27237q^{54} - 32235q^{55} - 49413q^{56} - 11676q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} + 79275q^{69} + 107079q^{70} + 31731q^{71} + 68229q^{72} - 1029q^{73} - 43680q^{74} - 73521q^{75} - 93954q^{76} - 90741q^{77} - 204498q^{78} - 61509q^{79} - 113421q^{80} - 98133q^{81} - 97671q^{82} - 27237q^{83} - 62811q^{84} + 28707q^{86} + 71358q^{87} + 83811q^{88} + 54411q^{89} + 292929q^{90} + 73563q^{91} + 198429q^{92} + 163947q^{93} + 161763q^{94} + 75579q^{95} + 213192q^{96} + 75579q^{97} + 51576q^{98} + 4095q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(43))\)

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
43.5.b \(\chi_{43}(42, \cdot)\) 43.5.b.a 1 1
43.5.b.b 12
43.5.d \(\chi_{43}(7, \cdot)\) 43.5.d.a 28 2
43.5.f \(\chi_{43}(2, \cdot)\) 43.5.f.a 78 6
43.5.h \(\chi_{43}(3, \cdot)\) 43.5.h.a 168 12