Properties

Label 100.9
Level 100
Weight 9
Dimension 1271
Nonzero newspaces 6
Newform subspaces 18
Sturm bound 5400
Trace bound 2

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 18 \)
Sturm bound: \(5400\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(100))\).

Total New Old
Modular forms 2470 1313 1157
Cusp forms 2330 1271 1059
Eisenstein series 140 42 98

Trace form

\( 1271 q - 10 q^{2} + 140 q^{3} + 142 q^{4} - 910 q^{5} + 2030 q^{6} + 4060 q^{7} - 6010 q^{8} - 289 q^{9} + O(q^{10}) \) \( 1271 q - 10 q^{2} + 140 q^{3} + 142 q^{4} - 910 q^{5} + 2030 q^{6} + 4060 q^{7} - 6010 q^{8} - 289 q^{9} + 24464 q^{10} + 840 q^{11} - 21690 q^{12} - 134910 q^{13} - 172826 q^{14} + 48478 q^{15} + 178062 q^{16} - 761480 q^{17} + 713670 q^{18} + 718900 q^{19} - 150126 q^{20} - 223376 q^{21} - 607050 q^{22} + 456240 q^{23} + 3652684 q^{24} + 643198 q^{25} - 1498636 q^{26} - 855730 q^{27} - 4673690 q^{28} - 3896706 q^{29} + 4819630 q^{30} + 3166524 q^{31} + 4154870 q^{32} + 7122080 q^{33} - 8846410 q^{34} - 3418728 q^{35} - 237498 q^{36} - 19733110 q^{37} + 17530100 q^{38} + 22510400 q^{39} + 1827404 q^{40} + 12698618 q^{41} - 56675270 q^{42} + 6309420 q^{43} - 9331720 q^{44} + 18719490 q^{45} + 23228090 q^{46} - 11954100 q^{47} + 76716340 q^{48} + 10309931 q^{49} - 60618206 q^{50} + 42485848 q^{51} - 107605580 q^{52} + 27444970 q^{53} - 5800552 q^{54} - 11288940 q^{55} + 46362290 q^{56} - 84097460 q^{57} + 76910900 q^{58} + 119809950 q^{59} + 8549610 q^{60} + 153479902 q^{61} - 173314600 q^{62} + 57553850 q^{63} - 71479688 q^{64} + 177500570 q^{65} + 21737870 q^{66} - 159630460 q^{67} + 41026790 q^{68} - 375700262 q^{69} + 19541830 q^{70} + 77172432 q^{71} + 79509200 q^{72} + 201619090 q^{73} - 14573060 q^{74} + 54011742 q^{75} + 134583460 q^{76} + 209455780 q^{77} + 167171040 q^{78} + 138506200 q^{79} + 13898694 q^{80} - 510388657 q^{81} - 25724370 q^{82} - 166486050 q^{83} - 821131802 q^{84} - 53211548 q^{85} - 233824150 q^{86} - 583747650 q^{87} + 615876510 q^{88} + 47700444 q^{89} + 1122304694 q^{90} + 347762196 q^{91} + 260716130 q^{92} - 32801930 q^{93} - 929235706 q^{94} + 256003896 q^{95} + 73649210 q^{96} + 1256639690 q^{97} + 8834530 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.9.b \(\chi_{100}(51, \cdot)\) 100.9.b.a 1 1
100.9.b.b 2
100.9.b.c 2
100.9.b.d 16
100.9.b.e 16
100.9.b.f 16
100.9.b.g 20
100.9.d \(\chi_{100}(99, \cdot)\) 100.9.d.a 2 1
100.9.d.b 4
100.9.d.c 32
100.9.d.d 32
100.9.f \(\chi_{100}(57, \cdot)\) 100.9.f.a 4 2
100.9.f.b 8
100.9.f.c 12
100.9.h \(\chi_{100}(19, \cdot)\) 100.9.h.a 472 4
100.9.j \(\chi_{100}(11, \cdot)\) 100.9.j.a 8 4
100.9.j.b 464
100.9.k \(\chi_{100}(13, \cdot)\) 100.9.k.a 160 8

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

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