Properties

Label 1920.2
Level 1920
Weight 2
Dimension 37728
Nonzero newspaces 36
Sturm bound 393216
Trace bound 81

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Defining parameters

Level: \( N \) = \( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(393216\)
Trace bound: \(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1920))\).

Total New Old
Modular forms 100864 38304 62560
Cusp forms 95745 37728 58017
Eisenstein series 5119 576 4543

Trace form

\( 37728 q - 24 q^{3} - 64 q^{4} - 96 q^{6} - 48 q^{7} - 40 q^{9} + O(q^{10}) \) \( 37728 q - 24 q^{3} - 64 q^{4} - 96 q^{6} - 48 q^{7} - 40 q^{9} - 96 q^{10} - 32 q^{12} - 64 q^{13} - 40 q^{15} - 192 q^{16} - 32 q^{18} - 48 q^{19} - 120 q^{21} - 64 q^{22} - 32 q^{23} - 32 q^{24} - 152 q^{25} - 72 q^{27} - 64 q^{28} - 64 q^{29} - 48 q^{30} - 224 q^{31} - 128 q^{33} - 64 q^{34} - 48 q^{35} - 96 q^{36} - 128 q^{37} - 72 q^{39} - 96 q^{40} - 64 q^{41} - 32 q^{42} - 80 q^{43} - 68 q^{45} - 192 q^{46} - 32 q^{48} + 16 q^{49} + 96 q^{50} - 64 q^{51} + 320 q^{52} + 128 q^{53} + 32 q^{54} - 8 q^{55} + 448 q^{56} + 88 q^{57} + 512 q^{58} + 128 q^{59} + 144 q^{60} + 64 q^{61} + 384 q^{62} + 48 q^{63} + 704 q^{64} + 128 q^{65} + 288 q^{66} + 112 q^{67} + 384 q^{68} + 120 q^{69} + 288 q^{70} + 128 q^{71} - 32 q^{72} + 176 q^{73} + 448 q^{74} - 4 q^{75} + 320 q^{76} + 128 q^{77} + 160 q^{78} + 32 q^{79} + 96 q^{80} - 80 q^{81} - 64 q^{82} - 32 q^{84} - 16 q^{85} + 88 q^{87} - 64 q^{88} - 48 q^{90} - 144 q^{91} + 64 q^{93} - 64 q^{94} - 96 q^{96} - 128 q^{97} + 104 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1920))\)

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
1920.2.a \(\chi_{1920}(1, \cdot)\) 1920.2.a.a 1 1
1920.2.a.b 1
1920.2.a.c 1
1920.2.a.d 1
1920.2.a.e 1
1920.2.a.f 1
1920.2.a.g 1
1920.2.a.h 1
1920.2.a.i 1
1920.2.a.j 1
1920.2.a.k 1
1920.2.a.l 1
1920.2.a.m 1
1920.2.a.n 1
1920.2.a.o 1
1920.2.a.p 1
1920.2.a.q 1
1920.2.a.r 1
1920.2.a.s 1
1920.2.a.t 1
1920.2.a.u 1
1920.2.a.v 1
1920.2.a.w 1
1920.2.a.x 1
1920.2.a.y 2
1920.2.a.z 2
1920.2.a.ba 2
1920.2.a.bb 2
1920.2.b \(\chi_{1920}(191, \cdot)\) 1920.2.b.a 8 1
1920.2.b.b 8
1920.2.b.c 8
1920.2.b.d 8
1920.2.b.e 8
1920.2.b.f 8
1920.2.b.g 8
1920.2.b.h 8
1920.2.d \(\chi_{1920}(1729, \cdot)\) 1920.2.d.a 4 1
1920.2.d.b 4
1920.2.d.c 6
1920.2.d.d 6
1920.2.d.e 6
1920.2.d.f 6
1920.2.d.g 8
1920.2.d.h 8
1920.2.f \(\chi_{1920}(769, \cdot)\) 1920.2.f.a 2 1
1920.2.f.b 2
1920.2.f.c 2
1920.2.f.d 2
1920.2.f.e 2
1920.2.f.f 2
1920.2.f.g 2
1920.2.f.h 2
1920.2.f.i 2
1920.2.f.j 2
1920.2.f.k 2
1920.2.f.l 2
1920.2.f.m 6
1920.2.f.n 6
1920.2.f.o 6
1920.2.f.p 6
1920.2.h \(\chi_{1920}(1151, \cdot)\) 1920.2.h.a 4 1
1920.2.h.b 4
1920.2.h.c 4
1920.2.h.d 4
1920.2.h.e 4
1920.2.h.f 4
1920.2.h.g 4
1920.2.h.h 4
1920.2.h.i 4
1920.2.h.j 4
1920.2.h.k 4
1920.2.h.l 4
1920.2.h.m 4
1920.2.h.n 4
1920.2.h.o 4
1920.2.h.p 4
1920.2.k \(\chi_{1920}(961, \cdot)\) 1920.2.k.a 2 1
1920.2.k.b 2
1920.2.k.c 2
1920.2.k.d 2
1920.2.k.e 2
1920.2.k.f 2
1920.2.k.g 2
1920.2.k.h 2
1920.2.k.i 4
1920.2.k.j 4
1920.2.k.k 4
1920.2.k.l 4
1920.2.m \(\chi_{1920}(959, \cdot)\) 1920.2.m.a 4 1
1920.2.m.b 4
1920.2.m.c 4
1920.2.m.d 4
1920.2.m.e 4
1920.2.m.f 4
1920.2.m.g 4
1920.2.m.h 4
1920.2.m.i 4
1920.2.m.j 4
1920.2.m.k 4
1920.2.m.l 4
1920.2.m.m 4
1920.2.m.n 4
1920.2.m.o 4
1920.2.m.p 4
1920.2.m.q 4
1920.2.m.r 4
1920.2.m.s 4
1920.2.m.t 4
1920.2.m.u 4
1920.2.m.v 4
1920.2.m.w 8
1920.2.o \(\chi_{1920}(1919, \cdot)\) 1920.2.o.a 24 1
1920.2.o.b 24
1920.2.o.c 24
1920.2.o.d 24
1920.2.s \(\chi_{1920}(481, \cdot)\) 1920.2.s.a 4 2
1920.2.s.b 4
1920.2.s.c 8
1920.2.s.d 8
1920.2.s.e 20
1920.2.s.f 20
1920.2.t \(\chi_{1920}(479, \cdot)\) n/a 176 2
1920.2.v \(\chi_{1920}(257, \cdot)\) n/a 192 2
1920.2.w \(\chi_{1920}(127, \cdot)\) 1920.2.w.a 4 2
1920.2.w.b 4
1920.2.w.c 4
1920.2.w.d 4
1920.2.w.e 8
1920.2.w.f 8
1920.2.w.g 8
1920.2.w.h 8
1920.2.w.i 12
1920.2.w.j 12
1920.2.w.k 12
1920.2.w.l 12
1920.2.y \(\chi_{1920}(223, \cdot)\) 1920.2.y.a 2 2
1920.2.y.b 2
1920.2.y.c 2
1920.2.y.d 2
1920.2.y.e 2
1920.2.y.f 2
1920.2.y.g 6
1920.2.y.h 6
1920.2.y.i 16
1920.2.y.j 16
1920.2.y.k 20
1920.2.y.l 20
1920.2.bb \(\chi_{1920}(737, \cdot)\) n/a 176 2
1920.2.bc \(\chi_{1920}(607, \cdot)\) 1920.2.bc.a 2 2
1920.2.bc.b 2
1920.2.bc.c 2
1920.2.bc.d 2
1920.2.bc.e 2
1920.2.bc.f 2
1920.2.bc.g 6
1920.2.bc.h 6
1920.2.bc.i 16
1920.2.bc.j 16
1920.2.bc.k 20
1920.2.bc.l 20
1920.2.bf \(\chi_{1920}(353, \cdot)\) n/a 176 2
1920.2.bh \(\chi_{1920}(703, \cdot)\) 1920.2.bh.a 4 2
1920.2.bh.b 4
1920.2.bh.c 4
1920.2.bh.d 4
1920.2.bh.e 4
1920.2.bh.f 4
1920.2.bh.g 4
1920.2.bh.h 4
1920.2.bh.i 8
1920.2.bh.j 8
1920.2.bh.k 12
1920.2.bh.l 12
1920.2.bh.m 12
1920.2.bh.n 12
1920.2.bi \(\chi_{1920}(833, \cdot)\) n/a 192 2
1920.2.bk \(\chi_{1920}(671, \cdot)\) n/a 128 2
1920.2.bl \(\chi_{1920}(289, \cdot)\) 1920.2.bl.a 48 2
1920.2.bl.b 48
1920.2.bo \(\chi_{1920}(367, \cdot)\) n/a 192 4
1920.2.br \(\chi_{1920}(497, \cdot)\) n/a 368 4
1920.2.bs \(\chi_{1920}(239, \cdot)\) n/a 368 4
1920.2.bv \(\chi_{1920}(241, \cdot)\) n/a 128 4
1920.2.bx \(\chi_{1920}(431, \cdot)\) n/a 256 4
1920.2.by \(\chi_{1920}(49, \cdot)\) n/a 192 4
1920.2.cb \(\chi_{1920}(17, \cdot)\) n/a 368 4
1920.2.cc \(\chi_{1920}(847, \cdot)\) n/a 192 4
1920.2.cf \(\chi_{1920}(233, \cdot)\) None 0 8
1920.2.cg \(\chi_{1920}(103, \cdot)\) None 0 8
1920.2.ci \(\chi_{1920}(121, \cdot)\) None 0 8
1920.2.ck \(\chi_{1920}(169, \cdot)\) None 0 8
1920.2.cn \(\chi_{1920}(71, \cdot)\) None 0 8
1920.2.cp \(\chi_{1920}(119, \cdot)\) None 0 8
1920.2.cr \(\chi_{1920}(137, \cdot)\) None 0 8
1920.2.cs \(\chi_{1920}(7, \cdot)\) None 0 8
1920.2.cw \(\chi_{1920}(173, \cdot)\) n/a 6080 16
1920.2.cx \(\chi_{1920}(163, \cdot)\) n/a 3072 16
1920.2.cy \(\chi_{1920}(11, \cdot)\) n/a 4096 16
1920.2.cz \(\chi_{1920}(109, \cdot)\) n/a 3072 16
1920.2.dc \(\chi_{1920}(61, \cdot)\) n/a 2048 16
1920.2.dd \(\chi_{1920}(59, \cdot)\) n/a 6080 16
1920.2.di \(\chi_{1920}(43, \cdot)\) n/a 3072 16
1920.2.dj \(\chi_{1920}(53, \cdot)\) n/a 6080 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 2}\)