↑

Properties

Label 200.3
Level 200
Weight 3
Dimension 1203
Nonzero newspaces 8
Newform subspaces 26
Sturm bound 7200
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 26 \)
Sturm bound: \(7200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(200))\).

Total New Old
Modular forms 2568 1285 1283
Cusp forms 2232 1203 1029
Eisenstein series 336 82 254

Trace form

\( 1203 q - 14 q^{2} - 14 q^{3} - 8 q^{4} - 4 q^{5} - 16 q^{6} - 28 q^{7} - 20 q^{8} - 29 q^{9} + O(q^{10}) \) \( 1203 q - 14 q^{2} - 14 q^{3} - 8 q^{4} - 4 q^{5} - 16 q^{6} - 28 q^{7} - 20 q^{8} - 29 q^{9} - 16 q^{10} + 10 q^{11} + 52 q^{12} + 76 q^{13} + 108 q^{14} + 56 q^{15} + 92 q^{16} + 6 q^{17} + 54 q^{18} - 38 q^{19} - 36 q^{20} - 112 q^{21} - 160 q^{22} - 204 q^{23} - 276 q^{24} - 82 q^{25} - 264 q^{26} - 152 q^{27} - 356 q^{28} - 260 q^{30} + 268 q^{31} - 324 q^{32} + 188 q^{33} - 336 q^{34} + 152 q^{35} - 232 q^{36} + 224 q^{37} + 32 q^{38} + 380 q^{39} + 24 q^{40} - 38 q^{41} + 268 q^{42} - 110 q^{43} + 452 q^{44} + 166 q^{45} + 636 q^{46} - 60 q^{47} + 1148 q^{48} + 25 q^{49} + 564 q^{50} - 68 q^{51} + 964 q^{52} - 48 q^{53} + 740 q^{54} - 268 q^{55} + 316 q^{56} - 292 q^{57} + 84 q^{58} - 486 q^{59} - 140 q^{60} - 192 q^{61} - 372 q^{62} - 1292 q^{63} - 788 q^{64} - 134 q^{65} - 1580 q^{66} - 974 q^{67} - 1556 q^{68} - 780 q^{70} - 1076 q^{71} - 1960 q^{72} - 18 q^{73} - 1292 q^{74} - 504 q^{75} - 640 q^{76} - 144 q^{77} - 484 q^{78} - 20 q^{79} - 76 q^{80} - 87 q^{81} - 464 q^{82} - 126 q^{83} - 820 q^{84} - 852 q^{85} + 88 q^{86} + 156 q^{87} - 916 q^{88} - 828 q^{89} - 1516 q^{90} + 492 q^{91} - 44 q^{92} - 960 q^{93} - 132 q^{94} + 92 q^{95} + 1060 q^{96} - 602 q^{97} - 214 q^{98} + 1202 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)

We only show spaces with odd 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
200.3.b \(\chi_{200}(151, \cdot)\) None 0 1
200.3.e \(\chi_{200}(99, \cdot)\) 200.3.e.a 2 1
200.3.e.b 4
200.3.e.c 12
200.3.e.d 16
200.3.g \(\chi_{200}(51, \cdot)\) 200.3.g.a 1 1
200.3.g.b 2
200.3.g.c 2
200.3.g.d 2
200.3.g.e 6
200.3.g.f 6
200.3.g.g 8
200.3.g.h 8
200.3.h \(\chi_{200}(199, \cdot)\) None 0 1
200.3.i \(\chi_{200}(93, \cdot)\) 200.3.i.a 16 2
200.3.i.b 20
200.3.i.c 32
200.3.l \(\chi_{200}(57, \cdot)\) 200.3.l.a 2 2
200.3.l.b 2
200.3.l.c 2
200.3.l.d 4
200.3.l.e 4
200.3.l.f 4
200.3.n \(\chi_{200}(11, \cdot)\) 200.3.n.a 232 4
200.3.p \(\chi_{200}(39, \cdot)\) None 0 4
200.3.r \(\chi_{200}(31, \cdot)\) None 0 4
200.3.s \(\chi_{200}(19, \cdot)\) 200.3.s.a 232 4
200.3.u \(\chi_{200}(17, \cdot)\) 200.3.u.a 56 8
200.3.u.b 64
200.3.x \(\chi_{200}(13, \cdot)\) 200.3.x.a 464 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)