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Properties

Label 3783.1
Level 3783
Weight 1
Dimension 386
Nonzero newspaces 30
Newform subspaces 50
Sturm bound 1053696
Trace bound 36

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Defining parameters

Level: \( N \) = \( 3783 = 3 \cdot 13 \cdot 97 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 50 \)
Sturm bound: \(1053696\)
Trace bound: \(36\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3783))\).

Total New Old
Modular forms 5026 2478 2548
Cusp forms 418 386 32
Eisenstein series 4608 2092 2516

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 370 8 8 0

Trace form

\( 386 q - 2 q^{3} + 24 q^{4} + 2 q^{7} + 8 q^{9} + O(q^{10}) \) \( 386 q - 2 q^{3} + 24 q^{4} + 2 q^{7} + 8 q^{9} - 8 q^{10} - 6 q^{12} + 4 q^{13} + 2 q^{15} + 4 q^{16} + 4 q^{19} - 16 q^{22} + 22 q^{25} - 2 q^{27} - 4 q^{28} + 8 q^{30} - 4 q^{31} + 4 q^{33} + 20 q^{36} - 2 q^{39} - 8 q^{40} - 6 q^{43} - 10 q^{48} + 10 q^{49} + 6 q^{52} - 12 q^{55} - 4 q^{60} + 2 q^{61} + 4 q^{63} + 14 q^{64} - 8 q^{66} - 4 q^{67} - 4 q^{69} - 4 q^{73} + 2 q^{75} - 2 q^{76} - 28 q^{79} + 28 q^{81} - 32 q^{84} - 4 q^{87} - 24 q^{88} + 8 q^{90} - 20 q^{91} - 32 q^{93} - 8 q^{94} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3783))\)

We only show spaces with odd 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
3783.1.c \(\chi_{3783}(1262, \cdot)\) None 0 1
3783.1.d \(\chi_{3783}(872, \cdot)\) None 0 1
3783.1.g \(\chi_{3783}(3782, \cdot)\) 3783.1.g.a 1 1
3783.1.g.b 1
3783.1.g.c 1
3783.1.g.d 1
3783.1.g.e 1
3783.1.g.f 1
3783.1.g.g 2
3783.1.g.h 2
3783.1.g.i 2
3783.1.g.j 2
3783.1.g.k 4
3783.1.g.l 4
3783.1.h \(\chi_{3783}(389, \cdot)\) None 0 1
3783.1.n \(\chi_{3783}(701, \cdot)\) 3783.1.n.a 2 2
3783.1.n.b 2
3783.1.n.c 4
3783.1.n.d 4
3783.1.o \(\chi_{3783}(1045, \cdot)\) None 0 2
3783.1.r \(\chi_{3783}(1165, \cdot)\) None 0 2
3783.1.s \(\chi_{3783}(775, \cdot)\) None 0 2
3783.1.v \(\chi_{3783}(463, \cdot)\) None 0 2
3783.1.w \(\chi_{3783}(560, \cdot)\) None 0 2
3783.1.z \(\chi_{3783}(1394, \cdot)\) 3783.1.z.a 2 2
3783.1.ba \(\chi_{3783}(35, \cdot)\) 3783.1.ba.a 2 2
3783.1.ba.b 4
3783.1.bc \(\chi_{3783}(290, \cdot)\) None 0 2
3783.1.be \(\chi_{3783}(1031, \cdot)\) 3783.1.be.a 2 2
3783.1.bf \(\chi_{3783}(740, \cdot)\) None 0 2
3783.1.bh \(\chi_{3783}(935, \cdot)\) None 0 2
3783.1.bj \(\chi_{3783}(62, \cdot)\) 3783.1.bj.a 2 2
3783.1.bk \(\chi_{3783}(680, \cdot)\) None 0 2
3783.1.bl \(\chi_{3783}(971, \cdot)\) None 0 2
3783.1.bn \(\chi_{3783}(230, \cdot)\) 3783.1.bn.a 2 2
3783.1.bp \(\chi_{3783}(521, \cdot)\) None 0 2
3783.1.bs \(\chi_{3783}(326, \cdot)\) None 0 2
3783.1.bu \(\chi_{3783}(1199, \cdot)\) 3783.1.bu.a 2 2
3783.1.bu.b 4
3783.1.bw \(\chi_{3783}(581, \cdot)\) None 0 2
3783.1.bx \(\chi_{3783}(3527, \cdot)\) 3783.1.bx.a 2 2
3783.1.by \(\chi_{3783}(1226, \cdot)\) 3783.1.by.a 2 2
3783.1.cb \(\chi_{3783}(2101, \cdot)\) None 0 4
3783.1.cc \(\chi_{3783}(1325, \cdot)\) 3783.1.cc.a 4 4
3783.1.cc.b 4
3783.1.cd \(\chi_{3783}(2198, \cdot)\) None 0 4
3783.1.cg \(\chi_{3783}(421, \cdot)\) None 0 4
3783.1.ci \(\chi_{3783}(1655, \cdot)\) 3783.1.ci.a 4 4
3783.1.ck \(\chi_{3783}(269, \cdot)\) None 0 4
3783.1.cn \(\chi_{3783}(404, \cdot)\) None 0 4
3783.1.cp \(\chi_{3783}(113, \cdot)\) 3783.1.cp.a 4 4
3783.1.cq \(\chi_{3783}(2710, \cdot)\) None 0 4
3783.1.ct \(\chi_{3783}(838, \cdot)\) None 0 4
3783.1.cu \(\chi_{3783}(934, \cdot)\) None 0 4
3783.1.cx \(\chi_{3783}(1051, \cdot)\) None 0 4
3783.1.cz \(\chi_{3783}(895, \cdot)\) None 0 4
3783.1.db \(\chi_{3783}(307, \cdot)\) None 0 4
3783.1.dd \(\chi_{3783}(760, \cdot)\) None 0 4
3783.1.de \(\chi_{3783}(643, \cdot)\) None 0 4
3783.1.dg \(\chi_{3783}(193, \cdot)\) None 0 4
3783.1.di \(\chi_{3783}(424, \cdot)\) None 0 4
3783.1.dl \(\chi_{3783}(229, \cdot)\) None 0 4
3783.1.dn \(\chi_{3783}(292, \cdot)\) None 0 4
3783.1.dp \(\chi_{3783}(1129, \cdot)\) None 0 4
3783.1.dq \(\chi_{3783}(3001, \cdot)\) None 0 4
3783.1.ds \(\chi_{3783}(889, \cdot)\) None 0 4
3783.1.du \(\chi_{3783}(604, \cdot)\) None 0 4
3783.1.dw \(\chi_{3783}(491, \cdot)\) 3783.1.dw.a 4 4
3783.1.dz \(\chi_{3783}(992, \cdot)\) None 0 4
3783.1.ea \(\chi_{3783}(857, \cdot)\) None 0 4
3783.1.ed \(\chi_{3783}(1277, \cdot)\) 3783.1.ed.a 4 4
3783.1.ef \(\chi_{3783}(794, \cdot)\) None 0 8
3783.1.eg \(\chi_{3783}(467, \cdot)\) 3783.1.eg.a 8 8
3783.1.eg.b 8
3783.1.ei \(\chi_{3783}(1279, \cdot)\) None 0 8
3783.1.el \(\chi_{3783}(70, \cdot)\) None 0 8
3783.1.em \(\chi_{3783}(397, \cdot)\) None 0 8
3783.1.eo \(\chi_{3783}(241, \cdot)\) None 0 8
3783.1.er \(\chi_{3783}(151, \cdot)\) None 0 8
3783.1.et \(\chi_{3783}(106, \cdot)\) None 0 8
3783.1.eu \(\chi_{3783}(140, \cdot)\) 3783.1.eu.a 8 8
3783.1.ev \(\chi_{3783}(1043, \cdot)\) 3783.1.ev.a 8 8
3783.1.fc \(\chi_{3783}(101, \cdot)\) 3783.1.fc.a 8 8
3783.1.fd \(\chi_{3783}(185, \cdot)\) 3783.1.fd.a 8 8
3783.1.fe \(\chi_{3783}(452, \cdot)\) None 0 8
3783.1.ff \(\chi_{3783}(341, \cdot)\) None 0 8
3783.1.fi \(\chi_{3783}(974, \cdot)\) None 0 8
3783.1.fj \(\chi_{3783}(170, \cdot)\) None 0 8
3783.1.fk \(\chi_{3783}(916, \cdot)\) None 0 8
3783.1.fn \(\chi_{3783}(535, \cdot)\) None 0 8
3783.1.fo \(\chi_{3783}(73, \cdot)\) None 0 8
3783.1.fr \(\chi_{3783}(1207, \cdot)\) None 0 8
3783.1.fs \(\chi_{3783}(125, \cdot)\) 3783.1.fs.a 16 16
3783.1.fs.b 16
3783.1.ft \(\chi_{3783}(164, \cdot)\) 3783.1.ft.a 16 16
3783.1.ft.b 16
3783.1.fw \(\chi_{3783}(142, \cdot)\) None 0 16
3783.1.fx \(\chi_{3783}(430, \cdot)\) None 0 16
3783.1.gb \(\chi_{3783}(335, \cdot)\) 3783.1.gb.a 16 16
3783.1.gc \(\chi_{3783}(419, \cdot)\) 3783.1.gc.a 16 16
3783.1.ge \(\chi_{3783}(613, \cdot)\) None 0 16
3783.1.gh \(\chi_{3783}(280, \cdot)\) None 0 16
3783.1.gi \(\chi_{3783}(31, \cdot)\) None 0 16
3783.1.gl \(\chi_{3783}(226, \cdot)\) None 0 16
3783.1.gn \(\chi_{3783}(53, \cdot)\) None 0 16
3783.1.go \(\chi_{3783}(584, \cdot)\) None 0 16
3783.1.gq \(\chi_{3783}(85, \cdot)\) None 0 16
3783.1.gr \(\chi_{3783}(145, \cdot)\) None 0 16
3783.1.gw \(\chi_{3783}(115, \cdot)\) None 0 16
3783.1.gx \(\chi_{3783}(163, \cdot)\) None 0 16
3783.1.ha \(\chi_{3783}(212, \cdot)\) None 0 16
3783.1.hb \(\chi_{3783}(380, \cdot)\) None 0 16
3783.1.hc \(\chi_{3783}(95, \cdot)\) 3783.1.hc.a 16 16
3783.1.hd \(\chi_{3783}(146, \cdot)\) 3783.1.hd.a 16 16
3783.1.hi \(\chi_{3783}(71, \cdot)\) 3783.1.hi.a 32 32
3783.1.hj \(\chi_{3783}(41, \cdot)\) 3783.1.hj.a 32 32
3783.1.ho \(\chi_{3783}(181, \cdot)\) None 0 32
3783.1.hp \(\chi_{3783}(55, \cdot)\) None 0 32
3783.1.hq \(\chi_{3783}(127, \cdot)\) None 0 32
3783.1.hr \(\chi_{3783}(40, \cdot)\) None 0 32
3783.1.hs \(\chi_{3783}(211, \cdot)\) None 0 32
3783.1.ht \(\chi_{3783}(10, \cdot)\) None 0 32
3783.1.ia \(\chi_{3783}(5, \cdot)\) None 0 32
3783.1.ib \(\chi_{3783}(20, \cdot)\) None 0 32
3783.1.ic \(\chi_{3783}(149, \cdot)\) None 0 32
3783.1.id \(\chi_{3783}(317, \cdot)\) None 0 32
3783.1.ie \(\chi_{3783}(332, \cdot)\) 3783.1.ie.a 32 32
3783.1.if \(\chi_{3783}(59, \cdot)\) 3783.1.if.a 32 32
3783.1.ik \(\chi_{3783}(217, \cdot)\) None 0 32
3783.1.il \(\chi_{3783}(82, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3783))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3783)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(97))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(291))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3783))\)\(^{\oplus 1}\)