Properties

Label 99.6
Level 99
Weight 6
Dimension 1362
Nonzero newspaces 8
Newform subspaces 21
Sturm bound 4320
Trace bound 2

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Defining parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 21 \)
Sturm bound: \(4320\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(99))\).

Total New Old
Modular forms 1880 1442 438
Cusp forms 1720 1362 358
Eisenstein series 160 80 80

Trace form

\( 1362 q - 33 q^{2} + 4 q^{3} + 75 q^{4} - 159 q^{5} - 362 q^{6} + 304 q^{7} + 1981 q^{8} + 808 q^{9} + O(q^{10}) \) \( 1362 q - 33 q^{2} + 4 q^{3} + 75 q^{4} - 159 q^{5} - 362 q^{6} + 304 q^{7} + 1981 q^{8} + 808 q^{9} - 1098 q^{10} - 1468 q^{11} - 5488 q^{12} - 422 q^{13} - 2814 q^{14} + 4084 q^{15} + 10975 q^{16} + 12216 q^{17} + 16180 q^{18} - 3072 q^{19} - 21380 q^{20} - 17360 q^{21} - 16980 q^{22} + 427 q^{23} + 802 q^{24} - 3619 q^{25} + 8170 q^{26} + 154 q^{27} - 602 q^{28} - 2210 q^{29} - 10868 q^{30} - 1619 q^{31} + 52504 q^{32} + 58350 q^{33} + 47044 q^{34} + 87008 q^{35} + 16838 q^{36} + 38317 q^{37} - 74288 q^{38} - 70790 q^{39} - 189274 q^{40} - 129846 q^{41} - 53336 q^{42} - 26484 q^{43} + 75184 q^{44} - 8406 q^{45} - 83230 q^{46} - 6934 q^{47} + 125030 q^{48} + 76294 q^{49} + 276637 q^{50} + 129062 q^{51} + 354396 q^{52} + 86576 q^{53} - 179982 q^{54} - 226281 q^{55} - 643080 q^{56} - 79344 q^{57} - 399970 q^{58} - 203025 q^{59} - 215136 q^{60} - 121830 q^{61} - 8628 q^{62} - 8748 q^{63} + 950243 q^{64} + 682818 q^{65} + 641648 q^{66} + 570617 q^{67} + 882194 q^{68} + 388344 q^{69} - 161962 q^{70} - 191829 q^{71} - 520772 q^{72} - 514404 q^{73} - 903960 q^{74} - 443806 q^{75} - 758910 q^{76} - 679224 q^{77} - 852984 q^{78} + 146192 q^{79} - 369246 q^{80} - 787784 q^{81} + 1908321 q^{82} + 215942 q^{83} + 578542 q^{84} - 413786 q^{85} + 830227 q^{86} + 1222992 q^{87} - 581866 q^{88} + 1131469 q^{89} + 2096564 q^{90} - 874744 q^{91} - 687728 q^{92} - 457716 q^{93} - 355572 q^{94} - 1139358 q^{95} - 2668726 q^{96} + 758799 q^{97} + 16796 q^{98} - 1554516 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)

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
99.6.a \(\chi_{99}(1, \cdot)\) 99.6.a.a 1 1
99.6.a.b 1
99.6.a.c 1
99.6.a.d 2
99.6.a.e 2
99.6.a.f 2
99.6.a.g 3
99.6.a.h 5
99.6.a.i 5
99.6.d \(\chi_{99}(98, \cdot)\) 99.6.d.a 20 1
99.6.e \(\chi_{99}(34, \cdot)\) 99.6.e.a 46 2
99.6.e.b 54
99.6.f \(\chi_{99}(37, \cdot)\) 99.6.f.a 16 4
99.6.f.b 20
99.6.f.c 20
99.6.f.d 40
99.6.g \(\chi_{99}(32, \cdot)\) 99.6.g.a 4 2
99.6.g.b 112
99.6.j \(\chi_{99}(8, \cdot)\) 99.6.j.a 80 4
99.6.m \(\chi_{99}(4, \cdot)\) 99.6.m.a 464 8
99.6.p \(\chi_{99}(2, \cdot)\) 99.6.p.a 464 8

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

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