Properties

Label 99.4
Level 99
Weight 4
Dimension 800
Nonzero newspaces 8
Newform subspaces 23
Sturm bound 2880
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 23 \)
Sturm bound: \(2880\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(99))\).

Total New Old
Modular forms 1160 880 280
Cusp forms 1000 800 200
Eisenstein series 160 80 80

Trace form

\( 800 q - 9 q^{2} - 14 q^{3} + 11 q^{4} + 15 q^{5} - 38 q^{6} - 51 q^{7} - 107 q^{8} - 110 q^{9} + O(q^{10}) \) \( 800 q - 9 q^{2} - 14 q^{3} + 11 q^{4} + 15 q^{5} - 38 q^{6} - 51 q^{7} - 107 q^{8} - 110 q^{9} + 26 q^{10} + 101 q^{11} + 272 q^{12} + 123 q^{13} - 90 q^{14} - 74 q^{15} - 537 q^{16} - 561 q^{17} - 452 q^{18} + 376 q^{19} + 556 q^{20} - 62 q^{21} + 582 q^{22} + 1096 q^{23} + 1378 q^{24} + 893 q^{25} + 1666 q^{26} + 784 q^{27} - 1994 q^{28} - 1367 q^{29} - 2156 q^{30} - 2135 q^{31} - 5096 q^{32} - 1818 q^{33} - 2176 q^{34} - 2557 q^{35} - 970 q^{36} - 405 q^{37} - 992 q^{38} - 1238 q^{39} + 3438 q^{40} + 3159 q^{41} + 3352 q^{42} + 3616 q^{43} + 5332 q^{44} + 2550 q^{45} + 1906 q^{46} + 1373 q^{47} + 662 q^{48} - 165 q^{49} + 1717 q^{50} + 836 q^{51} + 5540 q^{52} + 5069 q^{53} + 2910 q^{54} + 701 q^{55} + 3672 q^{56} + 2982 q^{57} - 370 q^{58} - 324 q^{59} - 4848 q^{60} - 2781 q^{61} - 13776 q^{62} - 5946 q^{63} - 10373 q^{64} - 9150 q^{65} - 7480 q^{66} - 5524 q^{67} - 12454 q^{68} - 6042 q^{69} - 10034 q^{70} - 10617 q^{71} - 5252 q^{72} - 3875 q^{73} + 2112 q^{74} + 2456 q^{75} + 5218 q^{76} + 8310 q^{77} + 11040 q^{78} + 5431 q^{79} + 14226 q^{80} - 206 q^{81} + 16715 q^{82} + 2696 q^{83} - 15794 q^{84} + 7373 q^{85} - 2939 q^{86} - 3114 q^{87} + 6846 q^{88} + 3904 q^{89} + 6692 q^{90} + 2259 q^{91} + 3784 q^{92} + 7206 q^{93} - 2340 q^{94} + 8241 q^{95} + 27530 q^{96} + 1132 q^{97} + 12362 q^{98} + 15363 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)

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
99.4.a \(\chi_{99}(1, \cdot)\) 99.4.a.a 1 1
99.4.a.b 1
99.4.a.c 2
99.4.a.d 2
99.4.a.e 2
99.4.a.f 2
99.4.a.g 2
99.4.d \(\chi_{99}(98, \cdot)\) 99.4.d.a 2 1
99.4.d.b 2
99.4.d.c 8
99.4.e \(\chi_{99}(34, \cdot)\) 99.4.e.a 2 2
99.4.e.b 24
99.4.e.c 34
99.4.f \(\chi_{99}(37, \cdot)\) 99.4.f.a 4 4
99.4.f.b 8
99.4.f.c 8
99.4.f.d 12
99.4.f.e 24
99.4.g \(\chi_{99}(32, \cdot)\) 99.4.g.a 4 2
99.4.g.b 64
99.4.j \(\chi_{99}(8, \cdot)\) 99.4.j.a 48 4
99.4.m \(\chi_{99}(4, \cdot)\) 99.4.m.a 272 8
99.4.p \(\chi_{99}(2, \cdot)\) 99.4.p.a 272 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 1}\)