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Properties

Label 1989.2
Level 1989
Weight 2
Dimension 111270
Nonzero newspaces 90
Sturm bound 580608
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1989 = 3^{2} \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 90 \)
Sturm bound: \(580608\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1989))\).

Total New Old
Modular forms 148224 114242 33982
Cusp forms 142081 111270 30811
Eisenstein series 6143 2972 3171

Trace form

\( 111270 q - 204 q^{2} - 272 q^{3} - 204 q^{4} - 204 q^{5} - 272 q^{6} - 200 q^{7} - 186 q^{8} - 272 q^{9} + O(q^{10}) \) \( 111270 q - 204 q^{2} - 272 q^{3} - 204 q^{4} - 204 q^{5} - 272 q^{6} - 200 q^{7} - 186 q^{8} - 272 q^{9} - 574 q^{10} - 176 q^{11} - 272 q^{12} - 196 q^{13} - 400 q^{14} - 272 q^{15} - 92 q^{16} - 197 q^{17} - 592 q^{18} - 556 q^{19} - 82 q^{20} - 272 q^{21} - 112 q^{22} - 164 q^{23} - 320 q^{24} - 106 q^{25} - 132 q^{26} - 608 q^{27} - 480 q^{28} - 206 q^{29} - 368 q^{30} - 200 q^{31} - 376 q^{32} - 344 q^{33} - 142 q^{34} - 536 q^{35} - 464 q^{36} - 626 q^{37} - 424 q^{38} - 432 q^{39} - 760 q^{40} - 410 q^{41} - 608 q^{42} - 272 q^{43} - 752 q^{44} - 520 q^{45} - 796 q^{46} - 504 q^{47} - 736 q^{48} - 392 q^{49} - 690 q^{50} - 448 q^{51} - 582 q^{52} - 528 q^{53} - 496 q^{54} - 608 q^{55} - 568 q^{56} - 432 q^{57} - 134 q^{58} - 248 q^{59} - 648 q^{60} - 90 q^{61} - 356 q^{62} - 464 q^{63} - 686 q^{64} - 342 q^{65} - 944 q^{66} - 204 q^{67} - 211 q^{68} - 736 q^{69} - 232 q^{70} - 372 q^{71} - 712 q^{72} - 660 q^{73} - 462 q^{74} - 512 q^{75} - 260 q^{76} - 296 q^{77} - 760 q^{78} - 400 q^{79} - 790 q^{80} - 464 q^{81} - 654 q^{82} - 464 q^{83} - 768 q^{84} - 393 q^{85} - 1232 q^{86} - 656 q^{87} - 624 q^{88} - 540 q^{89} - 1064 q^{90} - 824 q^{91} - 1160 q^{92} - 672 q^{93} - 652 q^{94} - 596 q^{95} - 568 q^{96} - 212 q^{97} - 900 q^{98} - 416 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1989))\)

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
1989.2.a \(\chi_{1989}(1, \cdot)\) 1989.2.a.a 1 1
1989.2.a.b 1
1989.2.a.c 1
1989.2.a.d 1
1989.2.a.e 1
1989.2.a.f 2
1989.2.a.g 2
1989.2.a.h 2
1989.2.a.i 3
1989.2.a.j 3
1989.2.a.k 3
1989.2.a.l 5
1989.2.a.m 5
1989.2.a.n 6
1989.2.a.o 6
1989.2.a.p 6
1989.2.a.q 8
1989.2.a.r 8
1989.2.a.s 8
1989.2.a.t 8
1989.2.b \(\chi_{1989}(766, \cdot)\) 1989.2.b.a 2 1
1989.2.b.b 2
1989.2.b.c 2
1989.2.b.d 4
1989.2.b.e 4
1989.2.b.f 6
1989.2.b.g 8
1989.2.b.h 8
1989.2.b.i 10
1989.2.b.j 10
1989.2.b.k 18
1989.2.b.l 18
1989.2.e \(\chi_{1989}(883, \cdot)\) n/a 104 1
1989.2.f \(\chi_{1989}(118, \cdot)\) 1989.2.f.a 2 1
1989.2.f.b 2
1989.2.f.c 2
1989.2.f.d 2
1989.2.f.e 4
1989.2.f.f 6
1989.2.f.g 6
1989.2.f.h 12
1989.2.f.i 16
1989.2.f.j 18
1989.2.f.k 20
1989.2.i \(\chi_{1989}(664, \cdot)\) n/a 384 2
1989.2.j \(\chi_{1989}(562, \cdot)\) n/a 448 2
1989.2.k \(\chi_{1989}(919, \cdot)\) n/a 188 2
1989.2.l \(\chi_{1989}(256, \cdot)\) n/a 448 2
1989.2.m \(\chi_{1989}(820, \cdot)\) n/a 180 2
1989.2.p \(\chi_{1989}(242, \cdot)\) n/a 168 2
1989.2.q \(\chi_{1989}(1412, \cdot)\) n/a 144 2
1989.2.t \(\chi_{1989}(1529, \cdot)\) n/a 168 2
1989.2.u \(\chi_{1989}(395, \cdot)\) n/a 168 2
1989.2.x \(\chi_{1989}(64, \cdot)\) n/a 208 2
1989.2.y \(\chi_{1989}(322, \cdot)\) n/a 496 2
1989.2.bb \(\chi_{1989}(205, \cdot)\) n/a 448 2
1989.2.bd \(\chi_{1989}(1036, \cdot)\) n/a 204 2
1989.2.bg \(\chi_{1989}(679, \cdot)\) n/a 496 2
1989.2.bi \(\chi_{1989}(781, \cdot)\) n/a 432 2
1989.2.bm \(\chi_{1989}(1531, \cdot)\) n/a 188 2
1989.2.bo \(\chi_{1989}(220, \cdot)\) n/a 496 2
1989.2.bq \(\chi_{1989}(628, \cdot)\) n/a 496 2
1989.2.br \(\chi_{1989}(511, \cdot)\) n/a 448 2
1989.2.bt \(\chi_{1989}(103, \cdot)\) n/a 448 2
1989.2.bv \(\chi_{1989}(1648, \cdot)\) n/a 208 2
1989.2.bz \(\chi_{1989}(16, \cdot)\) n/a 496 2
1989.2.cb \(\chi_{1989}(8, \cdot)\) n/a 336 4
1989.2.ce \(\chi_{1989}(586, \cdot)\) n/a 360 4
1989.2.cf \(\chi_{1989}(298, \cdot)\) n/a 408 4
1989.2.cg \(\chi_{1989}(161, \cdot)\) n/a 336 4
1989.2.cj \(\chi_{1989}(718, \cdot)\) n/a 992 4
1989.2.cl \(\chi_{1989}(361, \cdot)\) n/a 416 4
1989.2.cm \(\chi_{1989}(166, \cdot)\) n/a 992 4
1989.2.cp \(\chi_{1989}(259, \cdot)\) n/a 992 4
1989.2.cr \(\chi_{1989}(761, \cdot)\) n/a 992 4
1989.2.cs \(\chi_{1989}(713, \cdot)\) n/a 992 4
1989.2.cv \(\chi_{1989}(596, \cdot)\) n/a 896 4
1989.2.cw \(\chi_{1989}(149, \cdot)\) n/a 992 4
1989.2.cy \(\chi_{1989}(89, \cdot)\) n/a 336 4
1989.2.da \(\chi_{1989}(344, \cdot)\) n/a 992 4
1989.2.dc \(\chi_{1989}(47, \cdot)\) n/a 992 4
1989.2.df \(\chi_{1989}(86, \cdot)\) n/a 896 4
1989.2.dh \(\chi_{1989}(50, \cdot)\) n/a 992 4
1989.2.dj \(\chi_{1989}(305, \cdot)\) n/a 336 4
1989.2.dk \(\chi_{1989}(188, \cdot)\) n/a 304 4
1989.2.dm \(\chi_{1989}(137, \cdot)\) n/a 896 4
1989.2.do \(\chi_{1989}(203, \cdot)\) n/a 992 4
1989.2.dr \(\chi_{1989}(200, \cdot)\) n/a 992 4
1989.2.dt \(\chi_{1989}(752, \cdot)\) n/a 992 4
1989.2.dv \(\chi_{1989}(98, \cdot)\) n/a 336 4
1989.2.dw \(\chi_{1989}(157, \cdot)\) n/a 864 4
1989.2.dz \(\chi_{1989}(55, \cdot)\) n/a 408 4
1989.2.ea \(\chi_{1989}(412, \cdot)\) n/a 992 4
1989.2.ec \(\chi_{1989}(4, \cdot)\) n/a 992 4
1989.2.ef \(\chi_{1989}(116, \cdot)\) n/a 672 8
1989.2.eg \(\chi_{1989}(521, \cdot)\) n/a 576 8
1989.2.ei \(\chi_{1989}(226, \cdot)\) n/a 824 8
1989.2.el \(\chi_{1989}(73, \cdot)\) n/a 824 8
1989.2.em \(\chi_{1989}(2, \cdot)\) n/a 1984 8
1989.2.eo \(\chi_{1989}(434, \cdot)\) n/a 1984 8
1989.2.er \(\chi_{1989}(206, \cdot)\) n/a 672 8
1989.2.es \(\chi_{1989}(110, \cdot)\) n/a 1984 8
1989.2.eu \(\chi_{1989}(121, \cdot)\) n/a 1984 8
1989.2.ev \(\chi_{1989}(484, \cdot)\) n/a 1984 8
1989.2.fa \(\chi_{1989}(100, \cdot)\) n/a 832 8
1989.2.fb \(\chi_{1989}(127, \cdot)\) n/a 816 8
1989.2.fc \(\chi_{1989}(43, \cdot)\) n/a 1984 8
1989.2.fd \(\chi_{1989}(94, \cdot)\) n/a 1984 8
1989.2.fi \(\chi_{1989}(25, \cdot)\) n/a 1984 8
1989.2.fj \(\chi_{1989}(196, \cdot)\) n/a 1728 8
1989.2.fl \(\chi_{1989}(332, \cdot)\) n/a 672 8
1989.2.fm \(\chi_{1989}(461, \cdot)\) n/a 1984 8
1989.2.fp \(\chi_{1989}(83, \cdot)\) n/a 1984 8
1989.2.fr \(\chi_{1989}(383, \cdot)\) n/a 1984 8
1989.2.fs \(\chi_{1989}(58, \cdot)\) n/a 3968 16
1989.2.fv \(\chi_{1989}(175, \cdot)\) n/a 3968 16
1989.2.fx \(\chi_{1989}(29, \cdot)\) n/a 3968 16
1989.2.fy \(\chi_{1989}(95, \cdot)\) n/a 3968 16
1989.2.gb \(\chi_{1989}(14, \cdot)\) n/a 3456 16
1989.2.gc \(\chi_{1989}(194, \cdot)\) n/a 3968 16
1989.2.ge \(\chi_{1989}(163, \cdot)\) n/a 1648 16
1989.2.gf \(\chi_{1989}(124, \cdot)\) n/a 3968 16
1989.2.gk \(\chi_{1989}(7, \cdot)\) n/a 3968 16
1989.2.gl \(\chi_{1989}(28, \cdot)\) n/a 1648 16
1989.2.go \(\chi_{1989}(23, \cdot)\) n/a 3968 16
1989.2.gp \(\chi_{1989}(107, \cdot)\) n/a 1344 16
1989.2.gq \(\chi_{1989}(62, \cdot)\) n/a 1344 16
1989.2.gr \(\chi_{1989}(74, \cdot)\) n/a 3968 16
1989.2.gu \(\chi_{1989}(265, \cdot)\) n/a 3968 16
1989.2.gx \(\chi_{1989}(31, \cdot)\) n/a 3968 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1989))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1989)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)\(^{\oplus 2}\)