↑

Properties

Label 96.8
Level 96
Weight 8
Dimension 746
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 4096
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(4096\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(96))\).

Total New Old
Modular forms 1856 766 1090
Cusp forms 1728 746 982
Eisenstein series 128 20 108

Trace form

\( 746 q - 2 q^{3} - 8 q^{4} + 556 q^{5} - 4 q^{6} - 1380 q^{7} + 2230 q^{9} + O(q^{10}) \) \( 746 q - 2 q^{3} - 8 q^{4} + 556 q^{5} - 4 q^{6} - 1380 q^{7} + 2230 q^{9} + 25992 q^{10} - 30676 q^{12} - 27244 q^{13} + 52384 q^{14} + 13492 q^{15} + 105552 q^{16} - 11632 q^{17} - 40828 q^{18} - 60588 q^{19} - 164000 q^{20} + 29772 q^{21} + 748464 q^{22} + 430248 q^{23} - 380888 q^{24} - 188510 q^{25} + 727960 q^{26} - 714134 q^{27} + 390912 q^{28} + 120844 q^{29} - 869452 q^{30} + 1519436 q^{31} - 1071320 q^{32} + 490352 q^{33} + 402128 q^{34} - 1633008 q^{35} + 2399808 q^{36} - 413868 q^{37} + 1244920 q^{38} - 190612 q^{39} - 2686368 q^{40} + 373880 q^{41} + 1066016 q^{42} + 20476 q^{43} + 3370472 q^{44} - 1709144 q^{45} - 8 q^{46} + 1056408 q^{47} - 5044368 q^{48} - 1598226 q^{49} + 2317416 q^{50} - 1889232 q^{51} - 10204952 q^{52} + 4276284 q^{53} + 7603096 q^{54} + 3624504 q^{55} + 10737272 q^{56} - 4030904 q^{57} + 10358128 q^{58} + 3671872 q^{59} - 10832296 q^{60} + 13302212 q^{61} - 10347504 q^{62} - 3000564 q^{63} - 33831104 q^{64} + 2926136 q^{65} + 11246060 q^{66} + 2328812 q^{67} + 17922136 q^{68} - 11568324 q^{69} + 16298944 q^{70} + 19524712 q^{71} - 24248224 q^{72} - 14166372 q^{73} - 21862880 q^{74} - 11521578 q^{75} - 28887048 q^{76} + 43218752 q^{77} - 1095236 q^{78} + 13849788 q^{79} + 69474376 q^{80} + 14613186 q^{81} + 17660232 q^{82} - 25158808 q^{84} - 13883384 q^{85} - 39909568 q^{86} + 32887072 q^{87} - 63950752 q^{88} - 42762240 q^{89} - 35949664 q^{90} - 4997672 q^{91} - 684560 q^{92} + 33442344 q^{93} + 103147648 q^{94} + 69327376 q^{95} + 137949424 q^{96} + 52550324 q^{97} - 52426160 q^{98} - 24160532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(96))\)

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
96.8.a \(\chi_{96}(1, \cdot)\) 96.8.a.a 1 1
96.8.a.b 1
96.8.a.c 2
96.8.a.d 2
96.8.a.e 2
96.8.a.f 2
96.8.a.g 2
96.8.a.h 2
96.8.c \(\chi_{96}(95, \cdot)\) 96.8.c.a 28 1
96.8.d \(\chi_{96}(49, \cdot)\) 96.8.d.a 14 1
96.8.f \(\chi_{96}(47, \cdot)\) 96.8.f.a 2 1
96.8.f.b 4
96.8.f.c 20
96.8.j \(\chi_{96}(25, \cdot)\) None 0 2
96.8.k \(\chi_{96}(23, \cdot)\) None 0 2
96.8.n \(\chi_{96}(13, \cdot)\) 96.8.n.a 224 4
96.8.o \(\chi_{96}(11, \cdot)\) 96.8.o.a 440 4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(96))\) into lower level spaces

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