↑

Properties

Label 96.6
Level 96
Weight 6
Dimension 530
Nonzero newspaces 6
Newform subspaces 14
Sturm bound 3072
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 14 \)
Sturm bound: \(3072\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(96))\).

Total New Old
Modular forms 1344 550 794
Cusp forms 1216 530 686
Eisenstein series 128 20 108

Trace form

\( 530 q - 2 q^{3} - 8 q^{4} - 76 q^{5} - 4 q^{6} + 188 q^{7} - 50 q^{9} + O(q^{10}) \) \( 530 q - 2 q^{3} - 8 q^{4} - 76 q^{5} - 4 q^{6} + 188 q^{7} - 50 q^{9} + 392 q^{10} + 1580 q^{12} - 228 q^{13} - 4960 q^{14} - 908 q^{15} - 8368 q^{16} - 1616 q^{17} + 644 q^{18} + 2356 q^{19} + 15200 q^{20} + 2604 q^{21} + 24752 q^{22} - 5016 q^{23} - 21464 q^{24} - 30 q^{25} - 25960 q^{26} + 11194 q^{27} + 4352 q^{28} + 8564 q^{29} + 32564 q^{30} - 64820 q^{31} + 37160 q^{32} - 19384 q^{33} + 12496 q^{34} + 9552 q^{35} + 3264 q^{36} + 18812 q^{37} - 69640 q^{38} + 57068 q^{39} - 62368 q^{40} + 24232 q^{41} - 7264 q^{42} - 63492 q^{43} + 65512 q^{44} + 18064 q^{45} - 8 q^{46} - 65256 q^{47} + 112368 q^{48} - 76714 q^{49} + 137064 q^{50} + 27600 q^{51} - 73496 q^{52} + 174180 q^{53} - 144488 q^{54} - 116680 q^{55} - 150920 q^{56} - 53408 q^{57} - 26000 q^{58} + 57920 q^{59} + 143576 q^{60} - 162516 q^{61} + 175632 q^{62} + 47628 q^{63} + 98368 q^{64} - 127448 q^{65} + 145004 q^{66} + 73388 q^{67} + 310616 q^{68} + 144828 q^{69} + 112576 q^{70} - 15448 q^{71} + 179936 q^{72} - 53844 q^{73} - 426208 q^{74} - 237882 q^{75} - 512008 q^{76} - 325952 q^{77} - 611012 q^{78} + 103036 q^{79} + 584 q^{80} + 54474 q^{81} - 367288 q^{82} + 387560 q^{84} + 376088 q^{85} + 182080 q^{86} - 191360 q^{87} + 622944 q^{88} + 294912 q^{89} + 453536 q^{90} + 32824 q^{91} + 379376 q^{92} - 151608 q^{93} - 297600 q^{94} - 243184 q^{95} - 712976 q^{96} - 255804 q^{97} - 165808 q^{98} + 391180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(96))\)

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
96.6.a \(\chi_{96}(1, \cdot)\) 96.6.a.a 1 1
96.6.a.b 1
96.6.a.c 1
96.6.a.d 1
96.6.a.e 1
96.6.a.f 1
96.6.a.g 2
96.6.a.h 2
96.6.c \(\chi_{96}(95, \cdot)\) 96.6.c.a 20 1
96.6.d \(\chi_{96}(49, \cdot)\) 96.6.d.a 10 1
96.6.f \(\chi_{96}(47, \cdot)\) 96.6.f.a 2 1
96.6.f.b 16
96.6.j \(\chi_{96}(25, \cdot)\) None 0 2
96.6.k \(\chi_{96}(23, \cdot)\) None 0 2
96.6.n \(\chi_{96}(13, \cdot)\) 96.6.n.a 160 4
96.6.o \(\chi_{96}(11, \cdot)\) 96.6.o.a 312 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(96))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(96)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 1}\)