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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

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

Display 100 coefficients 10 coefficients

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 available 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