Properties

Label 198.6
Level 198
Weight 6
Dimension 1399
Nonzero newspaces 8
Sturm bound 12960
Trace bound 2

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Defining parameters

Level: \( N \) = \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(12960\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(198))\).

Total New Old
Modular forms 5560 1399 4161
Cusp forms 5240 1399 3841
Eisenstein series 320 0 320

Trace form

\( 1399 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} - 234 q^{7} - 128 q^{8} - 1158 q^{9} + O(q^{10}) \) \( 1399 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} - 234 q^{7} - 128 q^{8} - 1158 q^{9} - 8 q^{10} + 1223 q^{11} + 768 q^{12} + 918 q^{13} + 856 q^{14} - 5328 q^{15} + 1024 q^{16} - 9392 q^{17} - 5136 q^{18} + 5015 q^{19} + 1344 q^{20} + 22620 q^{21} + 4260 q^{22} - 23728 q^{23} - 1792 q^{24} + 5372 q^{25} + 15296 q^{26} + 3972 q^{27} + 9248 q^{28} + 10412 q^{29} - 18384 q^{30} - 2306 q^{31} - 11264 q^{32} - 98695 q^{33} - 25656 q^{34} - 92236 q^{35} + 16640 q^{36} - 20104 q^{37} + 152576 q^{38} + 169524 q^{39} + 43392 q^{40} + 164522 q^{41} - 40480 q^{42} + 13168 q^{43} - 81136 q^{44} - 171188 q^{45} - 80720 q^{46} - 181996 q^{47} - 7680 q^{48} - 52300 q^{49} + 64544 q^{50} - 21532 q^{51} + 72768 q^{52} + 235482 q^{53} + 233208 q^{54} + 336558 q^{55} + 48896 q^{56} + 108586 q^{57} + 416 q^{58} + 40743 q^{59} - 85248 q^{60} - 8146 q^{61} - 263224 q^{62} - 369896 q^{63} - 106496 q^{64} - 946452 q^{65} - 80064 q^{66} - 696860 q^{67} + 36064 q^{68} + 184 q^{69} + 465968 q^{70} + 740336 q^{71} + 119424 q^{72} + 726880 q^{73} + 222528 q^{74} + 654056 q^{75} + 53376 q^{76} + 770378 q^{77} - 481680 q^{78} - 176302 q^{79} - 116224 q^{80} + 846826 q^{81} - 860452 q^{82} - 680883 q^{83} - 309568 q^{84} + 281690 q^{85} - 578716 q^{86} - 1534108 q^{87} - 27200 q^{88} - 1336428 q^{89} - 327328 q^{90} + 1096892 q^{91} + 281952 q^{92} + 635360 q^{93} + 33520 q^{94} + 1502934 q^{95} - 24576 q^{96} - 1016083 q^{97} + 77076 q^{98} + 2439806 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(198))\)

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
198.6.a \(\chi_{198}(1, \cdot)\) 198.6.a.a 1 1
198.6.a.b 1
198.6.a.c 1
198.6.a.d 1
198.6.a.e 1
198.6.a.f 1
198.6.a.g 1
198.6.a.h 1
198.6.a.i 1
198.6.a.j 2
198.6.a.k 2
198.6.a.l 2
198.6.a.m 2
198.6.a.n 2
198.6.b \(\chi_{198}(197, \cdot)\) 198.6.b.a 10 1
198.6.b.b 10
198.6.e \(\chi_{198}(67, \cdot)\) 198.6.e.a 24 2
198.6.e.b 24
198.6.e.c 26
198.6.e.d 26
198.6.f \(\chi_{198}(37, \cdot)\) 198.6.f.a 8 4
198.6.f.b 8
198.6.f.c 8
198.6.f.d 12
198.6.f.e 12
198.6.f.f 12
198.6.f.g 20
198.6.f.h 20
198.6.i \(\chi_{198}(65, \cdot)\) n/a 120 2
198.6.l \(\chi_{198}(17, \cdot)\) 198.6.l.a 40 4
198.6.l.b 40
198.6.m \(\chi_{198}(25, \cdot)\) n/a 480 8
198.6.n \(\chi_{198}(29, \cdot)\) n/a 480 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(198))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(198)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)