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Properties

Label 1890.2
Level 1890
Weight 2
Dimension 21592
Nonzero newspaces 48
Sturm bound 373248
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(373248\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1890))\).

Total New Old
Modular forms 96192 21592 74600
Cusp forms 90433 21592 68841
Eisenstein series 5759 0 5759

Trace form

\( 21592 q + 4 q^{2} + 4 q^{4} - 12 q^{5} - 24 q^{6} - 8 q^{7} - 20 q^{8} - 48 q^{9} + O(q^{10}) \) \( 21592 q + 4 q^{2} + 4 q^{4} - 12 q^{5} - 24 q^{6} - 8 q^{7} - 20 q^{8} - 48 q^{9} - 28 q^{10} - 104 q^{11} - 12 q^{12} - 80 q^{13} - 48 q^{14} - 36 q^{15} - 4 q^{16} - 144 q^{17} + 24 q^{18} - 80 q^{19} - 4 q^{20} + 48 q^{21} - 64 q^{22} - 48 q^{23} - 60 q^{25} + 80 q^{26} + 108 q^{27} - 4 q^{28} + 48 q^{29} + 72 q^{30} - 80 q^{31} + 4 q^{32} + 156 q^{33} + 40 q^{34} + 66 q^{35} + 72 q^{36} + 188 q^{38} + 72 q^{39} + 52 q^{40} + 184 q^{41} + 48 q^{42} + 96 q^{43} + 80 q^{44} + 240 q^{45} + 96 q^{46} + 288 q^{47} + 24 q^{48} + 92 q^{49} + 348 q^{50} + 408 q^{51} + 112 q^{52} + 744 q^{53} + 216 q^{54} + 208 q^{55} + 32 q^{56} + 396 q^{57} + 256 q^{58} + 652 q^{59} + 72 q^{60} + 128 q^{61} + 368 q^{62} + 492 q^{63} - 20 q^{64} + 320 q^{65} + 288 q^{66} + 328 q^{67} + 252 q^{68} + 432 q^{69} + 142 q^{70} + 432 q^{71} + 96 q^{72} + 320 q^{73} + 384 q^{74} + 228 q^{75} + 116 q^{76} + 480 q^{77} + 288 q^{78} + 512 q^{79} + 24 q^{80} + 192 q^{81} + 56 q^{82} + 264 q^{83} + 216 q^{85} + 16 q^{86} + 384 q^{87} + 116 q^{88} + 356 q^{89} + 36 q^{90} + 100 q^{91} + 264 q^{93} + 152 q^{94} + 536 q^{95} + 24 q^{96} + 280 q^{97} + 148 q^{98} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1890))\)

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
1890.2.a \(\chi_{1890}(1, \cdot)\) 1890.2.a.a 1 1
1890.2.a.b 1
1890.2.a.c 1
1890.2.a.d 1
1890.2.a.e 1
1890.2.a.f 1
1890.2.a.g 1
1890.2.a.h 1
1890.2.a.i 1
1890.2.a.j 1
1890.2.a.k 1
1890.2.a.l 1
1890.2.a.m 1
1890.2.a.n 1
1890.2.a.o 1
1890.2.a.p 1
1890.2.a.q 1
1890.2.a.r 1
1890.2.a.s 1
1890.2.a.t 1
1890.2.a.u 1
1890.2.a.v 1
1890.2.a.w 1
1890.2.a.x 1
1890.2.a.y 2
1890.2.a.z 2
1890.2.a.ba 2
1890.2.a.bb 2
1890.2.b \(\chi_{1890}(1511, \cdot)\) 1890.2.b.a 8 1
1890.2.b.b 8
1890.2.b.c 12
1890.2.b.d 12
1890.2.d \(\chi_{1890}(1889, \cdot)\) 1890.2.d.a 8 1
1890.2.d.b 8
1890.2.d.c 8
1890.2.d.d 8
1890.2.d.e 16
1890.2.d.f 16
1890.2.g \(\chi_{1890}(379, \cdot)\) 1890.2.g.a 2 1
1890.2.g.b 2
1890.2.g.c 2
1890.2.g.d 2
1890.2.g.e 2
1890.2.g.f 2
1890.2.g.g 2
1890.2.g.h 2
1890.2.g.i 2
1890.2.g.j 2
1890.2.g.k 2
1890.2.g.l 2
1890.2.g.m 4
1890.2.g.n 4
1890.2.g.o 4
1890.2.g.p 4
1890.2.g.q 4
1890.2.g.r 4
1890.2.i \(\chi_{1890}(991, \cdot)\) 1890.2.i.a 2 2
1890.2.i.b 2
1890.2.i.c 2
1890.2.i.d 2
1890.2.i.e 4
1890.2.i.f 12
1890.2.i.g 12
1890.2.i.h 12
1890.2.i.i 16
1890.2.j \(\chi_{1890}(631, \cdot)\) 1890.2.j.a 2 2
1890.2.j.b 2
1890.2.j.c 2
1890.2.j.d 2
1890.2.j.e 2
1890.2.j.f 4
1890.2.j.g 4
1890.2.j.h 4
1890.2.j.i 6
1890.2.j.j 6
1890.2.j.k 6
1890.2.j.l 8
1890.2.k \(\chi_{1890}(541, \cdot)\) 1890.2.k.a 2 2
1890.2.k.b 2
1890.2.k.c 2
1890.2.k.d 2
1890.2.k.e 2
1890.2.k.f 2
1890.2.k.g 2
1890.2.k.h 2
1890.2.k.i 2
1890.2.k.j 2
1890.2.k.k 2
1890.2.k.l 2
1890.2.k.m 2
1890.2.k.n 2
1890.2.k.o 2
1890.2.k.p 2
1890.2.k.q 2
1890.2.k.r 2
1890.2.k.s 2
1890.2.k.t 2
1890.2.k.u 2
1890.2.k.v 2
1890.2.k.w 2
1890.2.k.x 2
1890.2.k.y 2
1890.2.k.z 2
1890.2.k.ba 2
1890.2.k.bb 2
1890.2.k.bc 2
1890.2.k.bd 2
1890.2.k.be 2
1890.2.k.bf 2
1890.2.k.bg 4
1890.2.k.bh 4
1890.2.k.bi 4
1890.2.k.bj 4
1890.2.k.bk 4
1890.2.k.bl 4
1890.2.l \(\chi_{1890}(361, \cdot)\) 1890.2.l.a 2 2
1890.2.l.b 2
1890.2.l.c 2
1890.2.l.d 2
1890.2.l.e 4
1890.2.l.f 12
1890.2.l.g 12
1890.2.l.h 12
1890.2.l.i 16
1890.2.m \(\chi_{1890}(323, \cdot)\) 1890.2.m.a 24 2
1890.2.m.b 24
1890.2.m.c 24
1890.2.m.d 24
1890.2.p \(\chi_{1890}(433, \cdot)\) n/a 128 2
1890.2.r \(\chi_{1890}(89, \cdot)\) 1890.2.r.a 48 2
1890.2.r.b 48
1890.2.t \(\chi_{1890}(1151, \cdot)\) 1890.2.t.a 4 2
1890.2.t.b 28
1890.2.t.c 32
1890.2.u \(\chi_{1890}(109, \cdot)\) n/a 128 2
1890.2.z \(\chi_{1890}(1009, \cdot)\) 1890.2.z.a 4 2
1890.2.z.b 24
1890.2.z.c 44
1890.2.ba \(\chi_{1890}(1369, \cdot)\) 1890.2.ba.a 96 2
1890.2.be \(\chi_{1890}(971, \cdot)\) 1890.2.be.a 4 2
1890.2.be.b 4
1890.2.be.c 8
1890.2.be.d 8
1890.2.be.e 8
1890.2.be.f 8
1890.2.be.g 12
1890.2.be.h 12
1890.2.be.i 12
1890.2.be.j 12
1890.2.bf \(\chi_{1890}(629, \cdot)\) 1890.2.bf.a 8 2
1890.2.bf.b 8
1890.2.bf.c 8
1890.2.bf.d 8
1890.2.bf.e 32
1890.2.bf.f 32
1890.2.bi \(\chi_{1890}(719, \cdot)\) 1890.2.bi.a 48 2
1890.2.bi.b 48
1890.2.bk \(\chi_{1890}(341, \cdot)\) 1890.2.bk.a 4 2
1890.2.bk.b 28
1890.2.bk.c 32
1890.2.bl \(\chi_{1890}(251, \cdot)\) 1890.2.bl.a 32 2
1890.2.bl.b 32
1890.2.bo \(\chi_{1890}(269, \cdot)\) n/a 128 2
1890.2.bq \(\chi_{1890}(289, \cdot)\) 1890.2.bq.a 96 2
1890.2.bs \(\chi_{1890}(211, \cdot)\) n/a 432 6
1890.2.bt \(\chi_{1890}(331, \cdot)\) n/a 576 6
1890.2.bu \(\chi_{1890}(121, \cdot)\) n/a 576 6
1890.2.bw \(\chi_{1890}(557, \cdot)\) n/a 192 4
1890.2.by \(\chi_{1890}(703, \cdot)\) n/a 256 4
1890.2.bz \(\chi_{1890}(73, \cdot)\) n/a 192 4
1890.2.cc \(\chi_{1890}(307, \cdot)\) n/a 192 4
1890.2.cd \(\chi_{1890}(197, \cdot)\) n/a 144 4
1890.2.cg \(\chi_{1890}(233, \cdot)\) n/a 192 4
1890.2.ch \(\chi_{1890}(53, \cdot)\) n/a 256 4
1890.2.cj \(\chi_{1890}(397, \cdot)\) n/a 192 4
1890.2.cm \(\chi_{1890}(479, \cdot)\) n/a 864 6
1890.2.co \(\chi_{1890}(499, \cdot)\) n/a 864 6
1890.2.cs \(\chi_{1890}(41, \cdot)\) n/a 576 6
1890.2.cu \(\chi_{1890}(311, \cdot)\) n/a 576 6
1890.2.cv \(\chi_{1890}(79, \cdot)\) n/a 864 6
1890.2.cx \(\chi_{1890}(169, \cdot)\) n/a 648 6
1890.2.cz \(\chi_{1890}(59, \cdot)\) n/a 864 6
1890.2.db \(\chi_{1890}(209, \cdot)\) n/a 864 6
1890.2.dd \(\chi_{1890}(101, \cdot)\) n/a 576 6
1890.2.dh \(\chi_{1890}(23, \cdot)\) n/a 1728 12
1890.2.di \(\chi_{1890}(13, \cdot)\) n/a 1728 12
1890.2.dj \(\chi_{1890}(157, \cdot)\) n/a 1728 12
1890.2.do \(\chi_{1890}(113, \cdot)\) n/a 1296 12
1890.2.dp \(\chi_{1890}(317, \cdot)\) n/a 1728 12
1890.2.dq \(\chi_{1890}(103, \cdot)\) n/a 1728 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1890))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1890)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(945))\)\(^{\oplus 2}\)