Properties

Label 2100.2
Level 2100
Weight 2
Dimension 44108
Nonzero newspaces 48
Sturm bound 460800
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(460800\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2100))\).

Total New Old
Modular forms 118560 44924 73636
Cusp forms 111841 44108 67733
Eisenstein series 6719 816 5903

Trace form

\( 44108 q + 9 q^{3} - 70 q^{4} + 4 q^{5} - 62 q^{6} - 54 q^{8} - 83 q^{9} + O(q^{10}) \) \( 44108 q + 9 q^{3} - 70 q^{4} + 4 q^{5} - 62 q^{6} - 54 q^{8} - 83 q^{9} - 96 q^{10} - 38 q^{11} - 50 q^{12} - 194 q^{13} - 24 q^{14} - 28 q^{15} - 78 q^{16} - 132 q^{17} + 30 q^{18} - 96 q^{19} + 40 q^{20} - 163 q^{21} - 60 q^{22} - 92 q^{23} + 106 q^{24} - 284 q^{25} + 94 q^{26} - 18 q^{27} + 38 q^{28} - 164 q^{29} + 44 q^{30} - 84 q^{31} + 110 q^{32} - 141 q^{33} + 136 q^{34} - 76 q^{35} + 10 q^{36} - 202 q^{37} + 202 q^{38} - 2 q^{39} + 176 q^{40} - 8 q^{41} + 138 q^{42} + 56 q^{43} + 304 q^{44} + 64 q^{45} + 120 q^{46} + 130 q^{47} + 218 q^{48} - 34 q^{49} + 328 q^{50} + 93 q^{51} + 384 q^{52} + 220 q^{53} + 68 q^{54} + 192 q^{55} + 202 q^{56} + 222 q^{57} + 408 q^{58} + 308 q^{59} + 164 q^{60} + 88 q^{61} + 408 q^{62} + 137 q^{63} + 326 q^{64} + 204 q^{65} + 86 q^{66} + 308 q^{67} + 428 q^{68} + 464 q^{69} + 276 q^{70} + 192 q^{71} + 146 q^{72} + 454 q^{73} + 462 q^{74} + 260 q^{75} + 364 q^{76} + 384 q^{77} + 240 q^{78} + 468 q^{79} + 224 q^{80} + 209 q^{81} + 428 q^{82} + 260 q^{83} + 84 q^{84} + 204 q^{85} + 142 q^{86} + 392 q^{87} + 168 q^{88} + 632 q^{89} - 28 q^{90} + 148 q^{91} - 260 q^{92} + 497 q^{93} - 280 q^{94} + 160 q^{95} - 34 q^{96} + 744 q^{97} - 274 q^{98} + 170 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2100))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2100.2.a \(\chi_{2100}(1, \cdot)\) 2100.2.a.a 1 1
2100.2.a.b 1
2100.2.a.c 1
2100.2.a.d 1
2100.2.a.e 1
2100.2.a.f 1
2100.2.a.g 1
2100.2.a.h 1
2100.2.a.i 1
2100.2.a.j 1
2100.2.a.k 1
2100.2.a.l 1
2100.2.a.m 1
2100.2.a.n 1
2100.2.a.o 1
2100.2.a.p 1
2100.2.a.q 1
2100.2.a.r 1
2100.2.c \(\chi_{2100}(1651, \cdot)\) n/a 152 1
2100.2.d \(\chi_{2100}(1301, \cdot)\) 2100.2.d.a 2 1
2100.2.d.b 2
2100.2.d.c 2
2100.2.d.d 2
2100.2.d.e 2
2100.2.d.f 4
2100.2.d.g 4
2100.2.d.h 4
2100.2.d.i 4
2100.2.d.j 8
2100.2.d.k 8
2100.2.d.l 8
2100.2.f \(\chi_{2100}(1049, \cdot)\) 2100.2.f.a 4 1
2100.2.f.b 4
2100.2.f.c 4
2100.2.f.d 4
2100.2.f.e 4
2100.2.f.f 4
2100.2.f.g 4
2100.2.f.h 4
2100.2.f.i 16
2100.2.i \(\chi_{2100}(1399, \cdot)\) n/a 144 1
2100.2.k \(\chi_{2100}(1849, \cdot)\) 2100.2.k.a 2 1
2100.2.k.b 2
2100.2.k.c 2
2100.2.k.d 2
2100.2.k.e 2
2100.2.k.f 2
2100.2.k.g 2
2100.2.k.h 2
2100.2.k.i 2
2100.2.k.j 2
2100.2.l \(\chi_{2100}(1499, \cdot)\) n/a 216 1
2100.2.n \(\chi_{2100}(1751, \cdot)\) n/a 228 1
2100.2.q \(\chi_{2100}(1201, \cdot)\) 2100.2.q.a 2 2
2100.2.q.b 2
2100.2.q.c 2
2100.2.q.d 2
2100.2.q.e 2
2100.2.q.f 4
2100.2.q.g 4
2100.2.q.h 4
2100.2.q.i 4
2100.2.q.j 4
2100.2.q.k 4
2100.2.q.l 8
2100.2.q.m 8
2100.2.s \(\chi_{2100}(1457, \cdot)\) 2100.2.s.a 16 2
2100.2.s.b 24
2100.2.s.c 32
2100.2.t \(\chi_{2100}(43, \cdot)\) n/a 216 2
2100.2.w \(\chi_{2100}(1007, \cdot)\) n/a 560 2
2100.2.x \(\chi_{2100}(1357, \cdot)\) 2100.2.x.a 8 2
2100.2.x.b 8
2100.2.x.c 16
2100.2.x.d 16
2100.2.z \(\chi_{2100}(421, \cdot)\) n/a 128 4
2100.2.bb \(\chi_{2100}(599, \cdot)\) n/a 560 2
2100.2.bc \(\chi_{2100}(949, \cdot)\) 2100.2.bc.a 4 2
2100.2.bc.b 4
2100.2.bc.c 4
2100.2.bc.d 4
2100.2.bc.e 8
2100.2.bc.f 8
2100.2.bc.g 8
2100.2.bc.h 8
2100.2.bg \(\chi_{2100}(851, \cdot)\) n/a 584 2
2100.2.bi \(\chi_{2100}(101, \cdot)\) 2100.2.bi.a 2 2
2100.2.bi.b 2
2100.2.bi.c 2
2100.2.bi.d 2
2100.2.bi.e 2
2100.2.bi.f 2
2100.2.bi.g 2
2100.2.bi.h 2
2100.2.bi.i 2
2100.2.bi.j 10
2100.2.bi.k 10
2100.2.bi.l 16
2100.2.bi.m 16
2100.2.bi.n 32
2100.2.bj \(\chi_{2100}(451, \cdot)\) n/a 304 2
2100.2.bl \(\chi_{2100}(199, \cdot)\) n/a 288 2
2100.2.bo \(\chi_{2100}(1349, \cdot)\) 2100.2.bo.a 4 2
2100.2.bo.b 4
2100.2.bo.c 4
2100.2.bo.d 4
2100.2.bo.e 4
2100.2.bo.f 4
2100.2.bo.g 20
2100.2.bo.h 20
2100.2.bo.i 32
2100.2.br \(\chi_{2100}(71, \cdot)\) n/a 1440 4
2100.2.bt \(\chi_{2100}(239, \cdot)\) n/a 1440 4
2100.2.bu \(\chi_{2100}(169, \cdot)\) n/a 112 4
2100.2.bw \(\chi_{2100}(139, \cdot)\) n/a 960 4
2100.2.bz \(\chi_{2100}(209, \cdot)\) n/a 320 4
2100.2.cb \(\chi_{2100}(41, \cdot)\) n/a 320 4
2100.2.cc \(\chi_{2100}(391, \cdot)\) n/a 960 4
2100.2.ce \(\chi_{2100}(157, \cdot)\) 2100.2.ce.a 8 4
2100.2.ce.b 8
2100.2.ce.c 24
2100.2.ce.d 24
2100.2.ce.e 32
2100.2.ch \(\chi_{2100}(143, \cdot)\) n/a 1120 4
2100.2.ci \(\chi_{2100}(907, \cdot)\) n/a 576 4
2100.2.cl \(\chi_{2100}(557, \cdot)\) n/a 192 4
2100.2.cm \(\chi_{2100}(121, \cdot)\) n/a 320 8
2100.2.co \(\chi_{2100}(13, \cdot)\) n/a 320 8
2100.2.cp \(\chi_{2100}(83, \cdot)\) n/a 3776 8
2100.2.cs \(\chi_{2100}(127, \cdot)\) n/a 1440 8
2100.2.ct \(\chi_{2100}(113, \cdot)\) n/a 480 8
2100.2.cv \(\chi_{2100}(89, \cdot)\) n/a 640 8
2100.2.cy \(\chi_{2100}(19, \cdot)\) n/a 1920 8
2100.2.da \(\chi_{2100}(31, \cdot)\) n/a 1920 8
2100.2.db \(\chi_{2100}(341, \cdot)\) n/a 640 8
2100.2.dd \(\chi_{2100}(11, \cdot)\) n/a 3776 8
2100.2.dh \(\chi_{2100}(109, \cdot)\) n/a 320 8
2100.2.di \(\chi_{2100}(179, \cdot)\) n/a 3776 8
2100.2.dk \(\chi_{2100}(53, \cdot)\) n/a 1280 16
2100.2.dn \(\chi_{2100}(67, \cdot)\) n/a 3840 16
2100.2.do \(\chi_{2100}(47, \cdot)\) n/a 7552 16
2100.2.dr \(\chi_{2100}(73, \cdot)\) n/a 640 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)