↑

Properties

Label 43.7
Level 43
Weight 7
Dimension 441
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 1078
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(1078\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(43))\).

Total New Old
Modular forms 483 483 0
Cusp forms 441 441 0
Eisenstein series 42 42 0

Trace form

\( 441 q - 21 q^{2} - 21 q^{3} - 21 q^{4} - 21 q^{5} - 21 q^{6} - 21 q^{7} - 21 q^{8} - 21 q^{9} + O(q^{10}) \) \( 441 q - 21 q^{2} - 21 q^{3} - 21 q^{4} - 21 q^{5} - 21 q^{6} - 21 q^{7} - 21 q^{8} - 21 q^{9} - 21 q^{10} - 21 q^{11} - 21 q^{12} - 21 q^{13} - 21 q^{14} - 21 q^{15} - 21 q^{16} - 21 q^{17} - 21 q^{18} - 21 q^{19} - 21 q^{20} - 21 q^{21} - 21 q^{22} - 21 q^{23} - 21 q^{24} - 21 q^{25} - 21 q^{26} - 21 q^{27} - 21 q^{28} - 21 q^{29} - 21 q^{30} + 194019 q^{31} + 114219 q^{32} - 326613 q^{33} - 574581 q^{34} - 230517 q^{35} - 21 q^{36} + 216699 q^{37} + 724395 q^{38} + 476259 q^{39} + 1403115 q^{40} + 102459 q^{41} - 564501 q^{43} - 860202 q^{44} - 1428861 q^{45} - 1229781 q^{46} - 267981 q^{47} - 1306389 q^{48} - 21 q^{49} + 809067 q^{50} + 816459 q^{51} + 3010539 q^{52} + 1193787 q^{53} + 1224699 q^{54} - 248997 q^{55} - 2304981 q^{56} - 952581 q^{57} - 21 q^{58} - 21 q^{59} - 21 q^{60} - 21 q^{61} - 21 q^{62} - 21 q^{63} - 21 q^{64} - 21 q^{65} - 21 q^{66} - 21 q^{67} - 21 q^{68} + 6157515 q^{69} + 2929479 q^{70} - 1249521 q^{71} - 12446091 q^{72} - 2683821 q^{73} - 7675920 q^{74} - 4593771 q^{75} - 972426 q^{76} + 2188347 q^{77} + 10252494 q^{78} + 4356051 q^{79} + 9932979 q^{80} + 9915339 q^{81} + 10899609 q^{82} + 3251619 q^{83} + 7876197 q^{84} - 3669981 q^{86} - 8959062 q^{87} - 10154445 q^{88} - 6156549 q^{89} - 30098271 q^{90} - 6569661 q^{91} - 14348691 q^{92} - 8379861 q^{93} - 3950877 q^{94} + 776979 q^{95} + 12537504 q^{96} + 10446387 q^{97} + 16960104 q^{98} + 20162205 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(43))\)

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
43.7.b \(\chi_{43}(42, \cdot)\) 43.7.b.a 1 1
43.7.b.b 20
43.7.d \(\chi_{43}(7, \cdot)\) 43.7.d.a 42 2
43.7.f \(\chi_{43}(2, \cdot)\) 43.7.f.a 126 6
43.7.h \(\chi_{43}(3, \cdot)\) 43.7.h.a 252 12