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

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

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 the 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

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