Properties

Label 3751.1
Level 3751
Weight 1
Dimension 230
Nonzero newspaces 24
Newform subspaces 36
Sturm bound 1161600
Trace bound 15

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3751 = 11^{2} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 36 \)
Sturm bound: \(1161600\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3751))\).

Total New Old
Modular forms 5061 4305 756
Cusp forms 261 230 31
Eisenstein series 4800 4075 725

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 210 0 20 0

Trace form

\( 230 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + q^{7} - q^{8} + 2 q^{9} + O(q^{10}) \) \( 230 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + q^{7} - q^{8} + 2 q^{9} - q^{10} - 8 q^{12} - q^{14} + 4 q^{15} + 2 q^{16} + q^{18} + q^{19} + 2 q^{20} + 12 q^{23} + 3 q^{25} - 11 q^{27} - q^{35} + 3 q^{36} - 13 q^{37} - q^{38} + q^{40} + q^{41} - 33 q^{45} + 2 q^{48} + q^{49} + 2 q^{53} - 39 q^{56} + 3 q^{59} + 4 q^{60} + q^{62} + q^{63} - 40 q^{67} + 4 q^{69} + q^{70} + 3 q^{71} - q^{72} - 9 q^{75} - 14 q^{80} + 4 q^{81} - q^{82} - 28 q^{89} - q^{90} + 2 q^{92} + 2 q^{93} + 2 q^{94} - q^{95} + 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3751))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3751.1.c \(\chi_{3751}(2419, \cdot)\) None 0 1
3751.1.d \(\chi_{3751}(1332, \cdot)\) 3751.1.d.a 1 1
3751.1.d.b 1
3751.1.d.c 2
3751.1.d.d 3
3751.1.d.e 3
3751.1.d.f 6
3751.1.l \(\chi_{3751}(1451, \cdot)\) 3751.1.l.a 4 2
3751.1.n \(\chi_{3751}(243, \cdot)\) 3751.1.n.a 2 2
3751.1.o \(\chi_{3751}(717, \cdot)\) 3751.1.o.a 4 4
3751.1.q \(\chi_{3751}(1170, \cdot)\) 3751.1.q.a 4 4
3751.1.r \(\chi_{3751}(27, \cdot)\) 3751.1.r.a 4 4
3751.1.s \(\chi_{3751}(511, \cdot)\) 3751.1.s.a 4 4
3751.1.t \(\chi_{3751}(2138, \cdot)\) 3751.1.t.a 4 4
3751.1.t.b 4
3751.1.t.c 4
3751.1.t.d 8
3751.1.t.e 12
3751.1.t.f 12
3751.1.t.g 24
3751.1.u \(\chi_{3751}(122, \cdot)\) 3751.1.u.a 4 4
3751.1.w \(\chi_{3751}(94, \cdot)\) None 0 4
3751.1.x \(\chi_{3751}(481, \cdot)\) 3751.1.x.a 4 4
3751.1.y \(\chi_{3751}(1492, \cdot)\) 3751.1.y.a 4 4
3751.1.z \(\chi_{3751}(1814, \cdot)\) None 0 4
3751.1.be \(\chi_{3751}(233, \cdot)\) 3751.1.be.a 4 4
3751.1.bf \(\chi_{3751}(1455, \cdot)\) 3751.1.bf.a 4 4
3751.1.bn \(\chi_{3751}(309, \cdot)\) None 0 10
3751.1.bp \(\chi_{3751}(32, \cdot)\) None 0 10
3751.1.br \(\chi_{3751}(360, \cdot)\) 3751.1.br.a 8 8
3751.1.bs \(\chi_{3751}(606, \cdot)\) 3751.1.bs.a 8 8
3751.1.bt \(\chi_{3751}(130, \cdot)\) 3751.1.bt.a 8 8
3751.1.bu \(\chi_{3751}(487, \cdot)\) 3751.1.bu.a 8 8
3751.1.bv \(\chi_{3751}(3, \cdot)\) 3751.1.bv.a 8 8
3751.1.bw \(\chi_{3751}(251, \cdot)\) 3751.1.bw.a 8 8
3751.1.bx \(\chi_{3751}(40, \cdot)\) 3751.1.bx.a 8 8
3751.1.cc \(\chi_{3751}(483, \cdot)\) None 0 8
3751.1.cd \(\chi_{3751}(112, \cdot)\) 3751.1.cd.a 8 8
3751.1.ce \(\chi_{3751}(578, \cdot)\) 3751.1.ce.a 8 8
3751.1.cf \(\chi_{3751}(118, \cdot)\) 3751.1.cf.a 8 8
3751.1.cf.b 16
3751.1.ch \(\chi_{3751}(323, \cdot)\) 3751.1.ch.a 8 8
3751.1.cp \(\chi_{3751}(254, \cdot)\) None 0 20
3751.1.cq \(\chi_{3751}(87, \cdot)\) None 0 20
3751.1.cs \(\chi_{3751}(15, \cdot)\) None 0 40
3751.1.cu \(\chi_{3751}(109, \cdot)\) None 0 40
3751.1.cv \(\chi_{3751}(2, \cdot)\) None 0 40
3751.1.cw \(\chi_{3751}(95, \cdot)\) None 0 40
3751.1.cx \(\chi_{3751}(63, \cdot)\) None 0 40
3751.1.dc \(\chi_{3751}(194, \cdot)\) None 0 40
3751.1.dd \(\chi_{3751}(58, \cdot)\) None 0 40
3751.1.de \(\chi_{3751}(23, \cdot)\) None 0 40
3751.1.df \(\chi_{3751}(92, \cdot)\) None 0 40
3751.1.dg \(\chi_{3751}(170, \cdot)\) None 0 40
3751.1.dh \(\chi_{3751}(201, \cdot)\) None 0 40
3751.1.di \(\chi_{3751}(35, \cdot)\) None 0 40
3751.1.dq \(\chi_{3751}(42, \cdot)\) None 0 80
3751.1.dr \(\chi_{3751}(50, \cdot)\) None 0 80
3751.1.dw \(\chi_{3751}(129, \cdot)\) None 0 80
3751.1.dx \(\chi_{3751}(173, \cdot)\) None 0 80
3751.1.dy \(\chi_{3751}(7, \cdot)\) None 0 80
3751.1.dz \(\chi_{3751}(10, \cdot)\) None 0 80
3751.1.eb \(\chi_{3751}(53, \cdot)\) None 0 80
3751.1.ec \(\chi_{3751}(137, \cdot)\) None 0 80
3751.1.ed \(\chi_{3751}(26, \cdot)\) None 0 80
3751.1.ee \(\chi_{3751}(12, \cdot)\) None 0 80
3751.1.ef \(\chi_{3751}(48, \cdot)\) None 0 80
3751.1.eh \(\chi_{3751}(18, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3751))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3751)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(341))\)\(^{\oplus 2}\)