Properties

Label 5292.2
Level 5292
Weight 2
Dimension 335493
Nonzero newspaces 64
Sturm bound 3048192

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(3048192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5292))\).

Total New Old
Modular forms 771048 338597 432451
Cusp forms 753049 335493 417556
Eisenstein series 17999 3104 14895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5292))\)

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
5292.2.a \(\chi_{5292}(1, \cdot)\) 5292.2.a.a 1 1
5292.2.a.b 1
5292.2.a.c 1
5292.2.a.d 1
5292.2.a.e 1
5292.2.a.f 1
5292.2.a.g 1
5292.2.a.h 1
5292.2.a.i 1
5292.2.a.j 1
5292.2.a.k 1
5292.2.a.l 1
5292.2.a.m 1
5292.2.a.n 2
5292.2.a.o 2
5292.2.a.p 2
5292.2.a.q 2
5292.2.a.r 2
5292.2.a.s 2
5292.2.a.t 2
5292.2.a.u 3
5292.2.a.v 3
5292.2.a.w 3
5292.2.a.x 3
5292.2.a.y 4
5292.2.a.z 4
5292.2.a.ba 4
5292.2.a.bb 4
5292.2.b \(\chi_{5292}(1567, \cdot)\) n/a 320 1
5292.2.e \(\chi_{5292}(1079, \cdot)\) n/a 328 1
5292.2.f \(\chi_{5292}(2645, \cdot)\) 5292.2.f.a 2 1
5292.2.f.b 2
5292.2.f.c 2
5292.2.f.d 4
5292.2.f.e 12
5292.2.f.f 16
5292.2.f.g 16
5292.2.i \(\chi_{5292}(1549, \cdot)\) 5292.2.i.a 2 2
5292.2.i.b 2
5292.2.i.c 2
5292.2.i.d 6
5292.2.i.e 6
5292.2.i.f 6
5292.2.i.g 6
5292.2.i.h 12
5292.2.i.i 14
5292.2.i.j 24
5292.2.j \(\chi_{5292}(1765, \cdot)\) 5292.2.j.a 2 2
5292.2.j.b 2
5292.2.j.c 2
5292.2.j.d 6
5292.2.j.e 6
5292.2.j.f 12
5292.2.j.g 14
5292.2.j.h 14
5292.2.j.i 24
5292.2.k \(\chi_{5292}(3889, \cdot)\) n/a 106 2
5292.2.l \(\chi_{5292}(361, \cdot)\) 5292.2.l.a 2 2
5292.2.l.b 2
5292.2.l.c 2
5292.2.l.d 6
5292.2.l.e 6
5292.2.l.f 6
5292.2.l.g 6
5292.2.l.h 12
5292.2.l.i 14
5292.2.l.j 24
5292.2.n \(\chi_{5292}(19, \cdot)\) n/a 464 2
5292.2.o \(\chi_{5292}(2627, \cdot)\) n/a 464 2
5292.2.t \(\chi_{5292}(2861, \cdot)\) n/a 106 2
5292.2.w \(\chi_{5292}(521, \cdot)\) 5292.2.w.a 16 2
5292.2.w.b 16
5292.2.w.c 48
5292.2.x \(\chi_{5292}(881, \cdot)\) 5292.2.x.a 16 2
5292.2.x.b 16
5292.2.x.c 48
5292.2.ba \(\chi_{5292}(2843, \cdot)\) n/a 472 2
5292.2.bb \(\chi_{5292}(1439, \cdot)\) n/a 464 2
5292.2.be \(\chi_{5292}(863, \cdot)\) n/a 640 2
5292.2.bf \(\chi_{5292}(1783, \cdot)\) n/a 640 2
5292.2.bi \(\chi_{5292}(3331, \cdot)\) n/a 464 2
5292.2.bj \(\chi_{5292}(1207, \cdot)\) n/a 464 2
5292.2.bm \(\chi_{5292}(2285, \cdot)\) 5292.2.bm.a 16 2
5292.2.bm.b 16
5292.2.bm.c 48
5292.2.bo \(\chi_{5292}(757, \cdot)\) n/a 444 6
5292.2.bp \(\chi_{5292}(589, \cdot)\) n/a 738 6
5292.2.bq \(\chi_{5292}(949, \cdot)\) n/a 720 6
5292.2.br \(\chi_{5292}(373, \cdot)\) n/a 720 6
5292.2.bu \(\chi_{5292}(377, \cdot)\) n/a 444 6
5292.2.bv \(\chi_{5292}(323, \cdot)\) n/a 2688 6
5292.2.by \(\chi_{5292}(55, \cdot)\) n/a 2688 6
5292.2.ca \(\chi_{5292}(263, \cdot)\) n/a 4272 6
5292.2.cb \(\chi_{5292}(607, \cdot)\) n/a 4272 6
5292.2.cf \(\chi_{5292}(293, \cdot)\) n/a 720 6
5292.2.ci \(\chi_{5292}(1685, \cdot)\) n/a 720 6
5292.2.ck \(\chi_{5292}(391, \cdot)\) n/a 4272 6
5292.2.cl \(\chi_{5292}(31, \cdot)\) n/a 4272 6
5292.2.cn \(\chi_{5292}(491, \cdot)\) n/a 4368 6
5292.2.cq \(\chi_{5292}(851, \cdot)\) n/a 4272 6
5292.2.cs \(\chi_{5292}(509, \cdot)\) n/a 720 6
5292.2.cu \(\chi_{5292}(289, \cdot)\) n/a 672 12
5292.2.cv \(\chi_{5292}(109, \cdot)\) n/a 900 12
5292.2.cw \(\chi_{5292}(253, \cdot)\) n/a 672 12
5292.2.cx \(\chi_{5292}(37, \cdot)\) n/a 672 12
5292.2.cz \(\chi_{5292}(17, \cdot)\) n/a 672 12
5292.2.dc \(\chi_{5292}(451, \cdot)\) n/a 3984 12
5292.2.dd \(\chi_{5292}(307, \cdot)\) n/a 3984 12
5292.2.dg \(\chi_{5292}(271, \cdot)\) n/a 5376 12
5292.2.dh \(\chi_{5292}(107, \cdot)\) n/a 5376 12
5292.2.dk \(\chi_{5292}(611, \cdot)\) n/a 3984 12
5292.2.dl \(\chi_{5292}(71, \cdot)\) n/a 3984 12
5292.2.do \(\chi_{5292}(125, \cdot)\) n/a 672 12
5292.2.dp \(\chi_{5292}(341, \cdot)\) n/a 672 12
5292.2.ds \(\chi_{5292}(269, \cdot)\) n/a 900 12
5292.2.dx \(\chi_{5292}(179, \cdot)\) n/a 3984 12
5292.2.dy \(\chi_{5292}(199, \cdot)\) n/a 3984 12
5292.2.ea \(\chi_{5292}(25, \cdot)\) n/a 6048 36
5292.2.eb \(\chi_{5292}(193, \cdot)\) n/a 6048 36
5292.2.ec \(\chi_{5292}(85, \cdot)\) n/a 6048 36
5292.2.ed \(\chi_{5292}(5, \cdot)\) n/a 6048 36
5292.2.eh \(\chi_{5292}(187, \cdot)\) n/a 36144 36
5292.2.ei \(\chi_{5292}(139, \cdot)\) n/a 36144 36
5292.2.ek \(\chi_{5292}(95, \cdot)\) n/a 36144 36
5292.2.en \(\chi_{5292}(155, \cdot)\) n/a 36144 36
5292.2.eq \(\chi_{5292}(173, \cdot)\) n/a 6048 36
5292.2.et \(\chi_{5292}(41, \cdot)\) n/a 6048 36
5292.2.eu \(\chi_{5292}(11, \cdot)\) n/a 36144 36
5292.2.ex \(\chi_{5292}(103, \cdot)\) n/a 36144 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5292))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5292)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2646))\)\(^{\oplus 2}\)