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Properties

Label 2100.4
Level 2100
Weight 4
Dimension 133138
Nonzero newspaces 48
Sturm bound 921600
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(921600\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2100))\).

Total New Old
Modular forms 348960 133954 215006
Cusp forms 342240 133138 209102
Eisenstein series 6720 816 5904

Trace form

\( 133138 q - 16 q^{3} - 54 q^{4} - 76 q^{5} - 46 q^{6} + 8 q^{7} + 234 q^{8} - 34 q^{9} + O(q^{10}) \) \( 133138 q - 16 q^{3} - 54 q^{4} - 76 q^{5} - 46 q^{6} + 8 q^{7} + 234 q^{8} - 34 q^{9} + 224 q^{10} + 320 q^{11} + 210 q^{12} - 464 q^{13} + 312 q^{14} - 8 q^{15} - 974 q^{16} - 24 q^{17} - 540 q^{18} + 136 q^{19} - 760 q^{20} + 38 q^{21} - 2044 q^{22} + 1220 q^{23} - 830 q^{24} + 796 q^{25} + 722 q^{26} - 2752 q^{27} + 662 q^{28} + 932 q^{29} + 124 q^{30} + 1128 q^{31} + 1150 q^{32} + 32 q^{33} - 1280 q^{34} + 664 q^{35} + 186 q^{36} + 1864 q^{37} + 3326 q^{38} + 5864 q^{39} + 3376 q^{40} - 1684 q^{41} - 1090 q^{42} + 456 q^{43} - 3472 q^{44} - 3756 q^{45} + 916 q^{46} - 8620 q^{47} - 8102 q^{48} - 4174 q^{49} - 11272 q^{50} - 464 q^{51} - 2672 q^{52} - 4924 q^{53} - 3652 q^{54} - 608 q^{55} + 12890 q^{56} - 1292 q^{57} + 17752 q^{58} + 7048 q^{59} + 15204 q^{60} + 4192 q^{61} + 9096 q^{62} + 3640 q^{63} + 4902 q^{64} + 2364 q^{65} - 1756 q^{66} - 11408 q^{67} - 10196 q^{68} - 2492 q^{69} - 19884 q^{70} - 4920 q^{71} - 9526 q^{72} - 15664 q^{73} - 22638 q^{74} - 6600 q^{75} - 12564 q^{76} - 5484 q^{77} - 7848 q^{78} + 9736 q^{79} - 416 q^{80} - 18838 q^{81} - 15612 q^{82} + 16384 q^{83} + 4808 q^{84} + 25044 q^{85} + 10922 q^{86} + 7800 q^{87} - 7960 q^{88} + 328 q^{89} - 6988 q^{90} - 11504 q^{91} + 13292 q^{92} - 16172 q^{93} + 27476 q^{94} - 12640 q^{95} + 4334 q^{96} - 28472 q^{97} + 31714 q^{98} - 1032 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2100))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2100.4.a \(\chi_{2100}(1, \cdot)\) 2100.4.a.a 1 1
2100.4.a.b 1
2100.4.a.c 1
2100.4.a.d 1
2100.4.a.e 1
2100.4.a.f 1
2100.4.a.g 1
2100.4.a.h 1
2100.4.a.i 1
2100.4.a.j 1
2100.4.a.k 1
2100.4.a.l 1
2100.4.a.m 1
2100.4.a.n 1
2100.4.a.o 2
2100.4.a.p 2
2100.4.a.q 2
2100.4.a.r 2
2100.4.a.s 2
2100.4.a.t 2
2100.4.a.u 2
2100.4.a.v 3
2100.4.a.w 3
2100.4.a.x 3
2100.4.a.y 3
2100.4.a.z 3
2100.4.a.ba 3
2100.4.a.bb 6
2100.4.a.bc 6
2100.4.c \(\chi_{2100}(1651, \cdot)\) n/a 456 1
2100.4.d \(\chi_{2100}(1301, \cdot)\) n/a 152 1
2100.4.f \(\chi_{2100}(1049, \cdot)\) n/a 144 1
2100.4.i \(\chi_{2100}(1399, \cdot)\) n/a 432 1
2100.4.k \(\chi_{2100}(1849, \cdot)\) 2100.4.k.a 2 1
2100.4.k.b 2
2100.4.k.c 2
2100.4.k.d 2
2100.4.k.e 2
2100.4.k.f 2
2100.4.k.g 2
2100.4.k.h 2
2100.4.k.i 2
2100.4.k.j 2
2100.4.k.k 4
2100.4.k.l 4
2100.4.k.m 4
2100.4.k.n 4
2100.4.k.o 4
2100.4.k.p 6
2100.4.k.q 6
2100.4.l \(\chi_{2100}(1499, \cdot)\) n/a 648 1
2100.4.n \(\chi_{2100}(1751, \cdot)\) n/a 684 1
2100.4.q \(\chi_{2100}(1201, \cdot)\) n/a 152 2
2100.4.s \(\chi_{2100}(1457, \cdot)\) n/a 216 2
2100.4.t \(\chi_{2100}(43, \cdot)\) n/a 648 2
2100.4.w \(\chi_{2100}(1007, \cdot)\) n/a 1712 2
2100.4.x \(\chi_{2100}(1357, \cdot)\) n/a 144 2
2100.4.z \(\chi_{2100}(421, \cdot)\) n/a 352 4
2100.4.bb \(\chi_{2100}(599, \cdot)\) n/a 1712 2
2100.4.bc \(\chi_{2100}(949, \cdot)\) n/a 144 2
2100.4.bg \(\chi_{2100}(851, \cdot)\) n/a 1800 2
2100.4.bi \(\chi_{2100}(101, \cdot)\) n/a 304 2
2100.4.bj \(\chi_{2100}(451, \cdot)\) n/a 912 2
2100.4.bl \(\chi_{2100}(199, \cdot)\) n/a 864 2
2100.4.bo \(\chi_{2100}(1349, \cdot)\) n/a 288 2
2100.4.br \(\chi_{2100}(71, \cdot)\) n/a 4320 4
2100.4.bt \(\chi_{2100}(239, \cdot)\) n/a 4320 4
2100.4.bu \(\chi_{2100}(169, \cdot)\) n/a 368 4
2100.4.bw \(\chi_{2100}(139, \cdot)\) n/a 2880 4
2100.4.bz \(\chi_{2100}(209, \cdot)\) n/a 960 4
2100.4.cb \(\chi_{2100}(41, \cdot)\) n/a 960 4
2100.4.cc \(\chi_{2100}(391, \cdot)\) n/a 2880 4
2100.4.ce \(\chi_{2100}(157, \cdot)\) n/a 288 4
2100.4.ch \(\chi_{2100}(143, \cdot)\) n/a 3424 4
2100.4.ci \(\chi_{2100}(907, \cdot)\) n/a 1728 4
2100.4.cl \(\chi_{2100}(557, \cdot)\) n/a 576 4
2100.4.cm \(\chi_{2100}(121, \cdot)\) n/a 960 8
2100.4.co \(\chi_{2100}(13, \cdot)\) n/a 960 8
2100.4.cp \(\chi_{2100}(83, \cdot)\) n/a 11456 8
2100.4.cs \(\chi_{2100}(127, \cdot)\) n/a 4320 8
2100.4.ct \(\chi_{2100}(113, \cdot)\) n/a 1440 8
2100.4.cv \(\chi_{2100}(89, \cdot)\) n/a 1920 8
2100.4.cy \(\chi_{2100}(19, \cdot)\) n/a 5760 8
2100.4.da \(\chi_{2100}(31, \cdot)\) n/a 5760 8
2100.4.db \(\chi_{2100}(341, \cdot)\) n/a 1920 8
2100.4.dd \(\chi_{2100}(11, \cdot)\) n/a 11456 8
2100.4.dh \(\chi_{2100}(109, \cdot)\) n/a 960 8
2100.4.di \(\chi_{2100}(179, \cdot)\) n/a 11456 8
2100.4.dk \(\chi_{2100}(53, \cdot)\) n/a 3840 16
2100.4.dn \(\chi_{2100}(67, \cdot)\) n/a 11520 16
2100.4.do \(\chi_{2100}(47, \cdot)\) n/a 22912 16
2100.4.dr \(\chi_{2100}(73, \cdot)\) n/a 1920 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2100))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2100)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2100))\)\(^{\oplus 1}\)