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Properties

Label 198.10
Level 198
Weight 10
Dimension 2521
Nonzero newspaces 8
Sturm bound 21600
Trace bound 2

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Defining parameters

Level: \( N \) = \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(21600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(198))\).

Total New Old
Modular forms 9880 2521 7359
Cusp forms 9560 2521 7039
Eisenstein series 320 0 320

Trace form

\( 2521 q + 32 q^{2} - 150 q^{3} + 2560 q^{4} + 6444 q^{5} + 6048 q^{6} + 3276 q^{7} - 16384 q^{8} - 27114 q^{9} + O(q^{10}) \) \( 2521 q + 32 q^{2} - 150 q^{3} + 2560 q^{4} + 6444 q^{5} + 6048 q^{6} + 3276 q^{7} - 16384 q^{8} - 27114 q^{9} + 133792 q^{10} + 89413 q^{11} - 150528 q^{12} + 38328 q^{13} + 679136 q^{14} + 2106252 q^{15} + 655360 q^{16} - 5554522 q^{17} - 847680 q^{18} + 795539 q^{19} + 1649664 q^{20} - 1011960 q^{21} - 999984 q^{22} - 1487138 q^{23} + 1949696 q^{24} - 29296898 q^{25} - 24042560 q^{26} - 157128 q^{27} + 15741440 q^{28} + 41549458 q^{29} + 23255616 q^{30} - 20112226 q^{31} - 13631488 q^{32} - 109973551 q^{33} - 35839008 q^{34} + 83337454 q^{35} + 18378752 q^{36} + 146963648 q^{37} + 81401152 q^{38} + 22087140 q^{39} - 89776128 q^{40} - 61180532 q^{41} + 2447744 q^{42} + 201845304 q^{43} + 55847680 q^{44} - 621533228 q^{45} + 156274368 q^{46} + 182212798 q^{47} + 48365568 q^{48} - 40096280 q^{49} - 63983456 q^{50} - 298752184 q^{51} + 116523008 q^{52} - 281679756 q^{53} - 384113952 q^{54} - 566862182 q^{55} + 132530176 q^{56} + 1074339742 q^{57} - 86126784 q^{58} + 1675918065 q^{59} - 143428608 q^{60} - 70078320 q^{61} - 1110744608 q^{62} - 2392128908 q^{63} - 738197504 q^{64} + 216111828 q^{65} + 840066048 q^{66} - 87950114 q^{67} - 193533952 q^{68} - 399641588 q^{69} - 1200784512 q^{70} - 744185048 q^{71} + 35364864 q^{72} + 1933522826 q^{73} + 1247487168 q^{74} + 1480761356 q^{75} + 748821504 q^{76} - 3349239698 q^{77} - 208914240 q^{78} + 394806596 q^{79} + 370671616 q^{80} + 2071927414 q^{81} + 57035312 q^{82} - 9195339363 q^{83} + 310264832 q^{84} - 510219020 q^{85} + 12460190032 q^{86} + 12638634152 q^{87} + 523595776 q^{88} - 1596593190 q^{89} - 9253656448 q^{90} + 8609717006 q^{91} - 6900907008 q^{92} - 10784318596 q^{93} - 2223835904 q^{94} + 422584584 q^{95} + 100663296 q^{96} + 1600723175 q^{97} + 12509809968 q^{98} + 27713994800 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(198))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
198.10.a \(\chi_{198}(1, \cdot)\) 198.10.a.a 1 1
198.10.a.b 1
198.10.a.c 1
198.10.a.d 1
198.10.a.e 1
198.10.a.f 1
198.10.a.g 1
198.10.a.h 2
198.10.a.i 2
198.10.a.j 2
198.10.a.k 2
198.10.a.l 2
198.10.a.m 2
198.10.a.n 2
198.10.a.o 2
198.10.a.p 3
198.10.a.q 3
198.10.a.r 4
198.10.a.s 4
198.10.b \(\chi_{198}(197, \cdot)\) 198.10.b.a 18 1
198.10.b.b 18
198.10.e \(\chi_{198}(67, \cdot)\) n/a 180 2
198.10.f \(\chi_{198}(37, \cdot)\) n/a 180 4
198.10.i \(\chi_{198}(65, \cdot)\) n/a 216 2
198.10.l \(\chi_{198}(17, \cdot)\) n/a 144 4
198.10.m \(\chi_{198}(25, \cdot)\) n/a 864 8
198.10.n \(\chi_{198}(29, \cdot)\) n/a 864 8

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(198))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(198)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)