Properties

Label 200.4
Level 200
Weight 4
Dimension 1826
Nonzero newspaces 10
Newform subspaces 44
Sturm bound 9600
Trace bound 3

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Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 44 \)
Sturm bound: \(9600\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(200))\).

Total New Old
Modular forms 3768 1908 1860
Cusp forms 3432 1826 1606
Eisenstein series 336 82 254

Trace form

\( 1826 q - 14 q^{2} - 16 q^{3} - 24 q^{4} + 11 q^{5} + 8 q^{6} - 28 q^{7} + 28 q^{8} - 127 q^{9} + O(q^{10}) \) \( 1826 q - 14 q^{2} - 16 q^{3} - 24 q^{4} + 11 q^{5} + 8 q^{6} - 28 q^{7} + 28 q^{8} - 127 q^{9} - 16 q^{10} - 120 q^{11} - 284 q^{12} - 86 q^{13} - 260 q^{14} + 56 q^{15} + 220 q^{16} + 170 q^{17} + 942 q^{18} + 480 q^{19} + 364 q^{20} + 656 q^{21} + 424 q^{22} + 4 q^{23} - 180 q^{24} - 137 q^{25} - 496 q^{26} - 1516 q^{27} - 676 q^{28} - 1350 q^{29} + 300 q^{30} - 1220 q^{31} + 316 q^{32} - 160 q^{33} - 560 q^{34} + 452 q^{35} - 1736 q^{36} + 939 q^{37} - 2344 q^{38} + 1356 q^{39} - 1576 q^{40} + 1334 q^{41} - 3156 q^{42} + 1936 q^{43} - 1420 q^{44} + 1991 q^{45} - 1492 q^{46} - 924 q^{47} - 1316 q^{48} - 1474 q^{49} + 164 q^{50} - 3276 q^{51} + 3412 q^{52} + 307 q^{53} + 5460 q^{54} + 1592 q^{55} + 4924 q^{56} + 3360 q^{57} + 4620 q^{58} + 3232 q^{59} + 3780 q^{60} + 622 q^{61} + 5900 q^{62} + 1596 q^{63} + 8172 q^{64} - 2129 q^{65} + 8308 q^{66} + 2000 q^{67} + 1772 q^{68} - 3472 q^{69} - 1660 q^{70} - 4460 q^{71} - 10248 q^{72} - 222 q^{73} - 11492 q^{74} - 4664 q^{75} - 7344 q^{76} + 2528 q^{77} - 12820 q^{78} - 6564 q^{79} - 3676 q^{80} + 4425 q^{81} + 4288 q^{82} + 1020 q^{83} + 4492 q^{84} + 7443 q^{85} - 2720 q^{86} + 764 q^{87} + 4460 q^{88} - 3897 q^{89} - 316 q^{90} + 1636 q^{91} + 2708 q^{92} - 5720 q^{93} - 6596 q^{94} - 4608 q^{95} + 9796 q^{96} - 6850 q^{97} - 6694 q^{98} - 10128 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.4.a \(\chi_{200}(1, \cdot)\) 200.4.a.a 1 1
200.4.a.b 1
200.4.a.c 1
200.4.a.d 1
200.4.a.e 1
200.4.a.f 1
200.4.a.g 1
200.4.a.h 1
200.4.a.i 1
200.4.a.j 1
200.4.a.k 2
200.4.a.l 2
200.4.c \(\chi_{200}(49, \cdot)\) 200.4.c.a 2 1
200.4.c.b 2
200.4.c.c 2
200.4.c.d 2
200.4.c.e 2
200.4.c.f 2
200.4.c.g 2
200.4.d \(\chi_{200}(101, \cdot)\) 200.4.d.a 2 1
200.4.d.b 12
200.4.d.c 12
200.4.d.d 12
200.4.d.e 16
200.4.f \(\chi_{200}(149, \cdot)\) 200.4.f.a 4 1
200.4.f.b 12
200.4.f.c 12
200.4.f.d 24
200.4.j \(\chi_{200}(7, \cdot)\) None 0 2
200.4.k \(\chi_{200}(43, \cdot)\) 200.4.k.a 2 2
200.4.k.b 2
200.4.k.c 2
200.4.k.d 2
200.4.k.e 4
200.4.k.f 4
200.4.k.g 8
200.4.k.h 16
200.4.k.i 32
200.4.k.j 32
200.4.m \(\chi_{200}(41, \cdot)\) 200.4.m.a 44 4
200.4.m.b 48
200.4.o \(\chi_{200}(29, \cdot)\) 200.4.o.a 352 4
200.4.q \(\chi_{200}(9, \cdot)\) 200.4.q.a 88 4
200.4.t \(\chi_{200}(21, \cdot)\) 200.4.t.a 352 4
200.4.v \(\chi_{200}(3, \cdot)\) 200.4.v.a 704 8
200.4.w \(\chi_{200}(23, \cdot)\) None 0 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 1}\)