# Properties

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

## 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

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