↑

Properties

Label 747.2
Level 747
Weight 2
Dimension 15990
Nonzero newspaces 8
Newform subspaces 27
Sturm bound 82656
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 747 = 3^{2} \cdot 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 27 \)
Sturm bound: \(82656\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(747))\).

Total New Old
Modular forms 21320 16718 4602
Cusp forms 20009 15990 4019
Eisenstein series 1311 728 583

Trace form

\( 15990 q - 123 q^{2} - 164 q^{3} - 123 q^{4} - 123 q^{5} - 164 q^{6} - 123 q^{7} - 123 q^{8} - 164 q^{9} + O(q^{10}) \) \( 15990 q - 123 q^{2} - 164 q^{3} - 123 q^{4} - 123 q^{5} - 164 q^{6} - 123 q^{7} - 123 q^{8} - 164 q^{9} - 369 q^{10} - 123 q^{11} - 164 q^{12} - 123 q^{13} - 123 q^{14} - 164 q^{15} - 123 q^{16} - 123 q^{17} - 164 q^{18} - 369 q^{19} - 123 q^{20} - 164 q^{21} - 123 q^{22} - 123 q^{23} - 164 q^{24} - 123 q^{25} - 123 q^{26} - 164 q^{27} - 369 q^{28} - 123 q^{29} - 164 q^{30} - 123 q^{31} - 123 q^{32} - 164 q^{33} - 123 q^{34} - 123 q^{35} - 164 q^{36} - 369 q^{37} - 123 q^{38} - 164 q^{39} - 123 q^{40} - 123 q^{41} - 164 q^{42} - 123 q^{43} - 123 q^{44} - 164 q^{45} - 369 q^{46} - 123 q^{47} - 164 q^{48} - 123 q^{49} - 123 q^{50} - 164 q^{51} - 123 q^{52} - 123 q^{53} - 164 q^{54} - 369 q^{55} - 123 q^{56} - 164 q^{57} - 123 q^{58} - 123 q^{59} - 164 q^{60} - 123 q^{61} - 123 q^{62} - 164 q^{63} - 369 q^{64} - 123 q^{65} - 164 q^{66} - 164 q^{67} - 287 q^{68} - 164 q^{69} - 287 q^{70} - 164 q^{71} - 164 q^{72} - 492 q^{73} - 205 q^{74} - 164 q^{75} - 287 q^{76} - 246 q^{77} - 164 q^{78} - 246 q^{79} - 533 q^{80} - 164 q^{81} - 574 q^{82} - 246 q^{83} - 328 q^{84} - 246 q^{85} - 287 q^{86} - 164 q^{87} - 533 q^{88} - 246 q^{89} - 164 q^{90} - 492 q^{91} - 287 q^{92} - 164 q^{93} - 205 q^{94} - 246 q^{95} - 164 q^{96} - 164 q^{97} - 287 q^{98} - 164 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(747))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
747.2.a \(\chi_{747}(1, \cdot)\) 747.2.a.a 1 1
747.2.a.b 1
747.2.a.c 1
747.2.a.d 1
747.2.a.e 1
747.2.a.f 2
747.2.a.g 4
747.2.a.h 5
747.2.a.i 6
747.2.a.j 6
747.2.a.k 6
747.2.d \(\chi_{747}(746, \cdot)\) 747.2.d.a 28 1
747.2.e \(\chi_{747}(250, \cdot)\) 747.2.e.a 2 2
747.2.e.b 2
747.2.e.c 2
747.2.e.d 4
747.2.e.e 62
747.2.e.f 92
747.2.f \(\chi_{747}(248, \cdot)\) 747.2.f.a 12 2
747.2.f.b 152
747.2.i \(\chi_{747}(10, \cdot)\) 747.2.i.a 240 40
747.2.i.b 280
747.2.i.c 280
747.2.i.d 560
747.2.j \(\chi_{747}(8, \cdot)\) 747.2.j.a 1120 40
747.2.m \(\chi_{747}(4, \cdot)\) 747.2.m.a 6560 80
747.2.p \(\chi_{747}(2, \cdot)\) 747.2.p.a 6560 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(747))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(747)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(249))\)\(^{\oplus 2}\)