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Properties

Label 198.2
Level 198
Weight 2
Dimension 281
Nonzero newspaces 8
Newform subspaces 25
Sturm bound 4320
Trace bound 2

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Defining parameters

Level: \( N \) = \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 25 \)
Sturm bound: \(4320\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(198))\).

Total New Old
Modular forms 1240 281 959
Cusp forms 921 281 640
Eisenstein series 319 0 319

Trace form

\( 281 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 14 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 281 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 14 q^{7} - 4 q^{8} - 6 q^{9} + 10 q^{10} + 7 q^{11} + 14 q^{13} + 14 q^{14} + 2 q^{16} + 32 q^{17} + 12 q^{18} + 19 q^{19} - 12 q^{21} - 3 q^{22} - 32 q^{23} - 4 q^{24} - 50 q^{25} - 68 q^{26} - 60 q^{27} - 38 q^{28} - 68 q^{29} - 60 q^{30} - 58 q^{31} - 13 q^{32} - 91 q^{33} - 66 q^{34} - 140 q^{35} - 16 q^{36} - 44 q^{37} - 92 q^{38} - 60 q^{39} - 30 q^{40} - 62 q^{41} - 40 q^{42} - 32 q^{43} + q^{44} - 20 q^{45} + 44 q^{46} + 28 q^{47} - 6 q^{48} + 54 q^{49} + 10 q^{50} - 28 q^{51} + 24 q^{52} - 78 q^{53} - 18 q^{54} - 10 q^{55} + 4 q^{56} - 86 q^{57} + 52 q^{58} - 69 q^{59} + 6 q^{61} + 46 q^{62} - 56 q^{63} - 4 q^{64} - 60 q^{65} - 60 q^{67} + 14 q^{68} - 80 q^{69} + 40 q^{70} - 32 q^{71} - 6 q^{72} - 64 q^{73} + 12 q^{74} - 40 q^{75} + 8 q^{76} - 86 q^{77} + 12 q^{78} - 38 q^{79} + 10 q^{80} + 58 q^{81} - 61 q^{82} + 129 q^{83} + 92 q^{84} + 30 q^{85} + 133 q^{86} + 164 q^{87} + 7 q^{88} + 156 q^{89} + 200 q^{90} - 156 q^{91} + 78 q^{92} + 200 q^{93} - 32 q^{94} + 270 q^{95} + 25 q^{97} + 147 q^{98} + 302 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)

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
198.2.a \(\chi_{198}(1, \cdot)\) 198.2.a.a 1 1
198.2.a.b 1
198.2.a.c 1
198.2.a.d 1
198.2.a.e 1
198.2.b \(\chi_{198}(197, \cdot)\) 198.2.b.a 2 1
198.2.b.b 2
198.2.e \(\chi_{198}(67, \cdot)\) 198.2.e.a 2 2
198.2.e.b 2
198.2.e.c 4
198.2.e.d 6
198.2.e.e 6
198.2.f \(\chi_{198}(37, \cdot)\) 198.2.f.a 4 4
198.2.f.b 4
198.2.f.c 4
198.2.f.d 4
198.2.f.e 4
198.2.i \(\chi_{198}(65, \cdot)\) 198.2.i.a 12 2
198.2.i.b 12
198.2.l \(\chi_{198}(17, \cdot)\) 198.2.l.a 8 4
198.2.l.b 8
198.2.m \(\chi_{198}(25, \cdot)\) 198.2.m.a 40 8
198.2.m.b 56
198.2.n \(\chi_{198}(29, \cdot)\) 198.2.n.a 48 8
198.2.n.b 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(198))\) into lower level spaces

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