# Properties

 Label 5796.2 Level 5796 Weight 2 Dimension 400372 Nonzero newspaces 80 Sturm bound 3649536

## Defining parameters

 Level: $$N$$ = $$5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$3649536$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5796))$$.

Total New Old
Modular forms 922944 404148 518796
Cusp forms 901825 400372 501453
Eisenstein series 21119 3776 17343

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5796))$$

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
5796.2.a $$\chi_{5796}(1, \cdot)$$ 5796.2.a.a 1 1
5796.2.a.b 1
5796.2.a.c 1
5796.2.a.d 1
5796.2.a.e 1
5796.2.a.f 1
5796.2.a.g 1
5796.2.a.h 1
5796.2.a.i 2
5796.2.a.j 2
5796.2.a.k 2
5796.2.a.l 2
5796.2.a.m 2
5796.2.a.n 2
5796.2.a.o 3
5796.2.a.p 3
5796.2.a.q 4
5796.2.a.r 4
5796.2.a.s 5
5796.2.a.t 5
5796.2.a.u 6
5796.2.a.v 6
5796.2.b $$\chi_{5796}(5795, \cdot)$$ n/a 384 1
5796.2.c $$\chi_{5796}(2071, \cdot)$$ n/a 440 1
5796.2.h $$\chi_{5796}(323, \cdot)$$ n/a 264 1
5796.2.i $$\chi_{5796}(3403, \cdot)$$ n/a 360 1
5796.2.j $$\chi_{5796}(2393, \cdot)$$ 5796.2.j.a 56 1
5796.2.k $$\chi_{5796}(5473, \cdot)$$ 5796.2.k.a 8 1
5796.2.k.b 16
5796.2.k.c 24
5796.2.k.d 32
5796.2.p $$\chi_{5796}(3725, \cdot)$$ 5796.2.p.a 48 1
5796.2.q $$\chi_{5796}(277, \cdot)$$ n/a 352 2
5796.2.r $$\chi_{5796}(1933, \cdot)$$ n/a 264 2
5796.2.s $$\chi_{5796}(3313, \cdot)$$ n/a 148 2
5796.2.t $$\chi_{5796}(2209, \cdot)$$ n/a 352 2
5796.2.w $$\chi_{5796}(691, \cdot)$$ n/a 2112 2
5796.2.x $$\chi_{5796}(551, \cdot)$$ n/a 2288 2
5796.2.y $$\chi_{5796}(2851, \cdot)$$ n/a 2288 2
5796.2.z $$\chi_{5796}(599, \cdot)$$ n/a 2112 2
5796.2.be $$\chi_{5796}(137, \cdot)$$ n/a 384 2
5796.2.bf $$\chi_{5796}(1793, \cdot)$$ n/a 288 2
5796.2.bk $$\chi_{5796}(1241, \cdot)$$ n/a 128 2
5796.2.bl $$\chi_{5796}(1333, \cdot)$$ n/a 160 2
5796.2.bm $$\chi_{5796}(4049, \cdot)$$ n/a 120 2
5796.2.br $$\chi_{5796}(229, \cdot)$$ n/a 384 2
5796.2.bs $$\chi_{5796}(1013, \cdot)$$ n/a 352 2
5796.2.bt $$\chi_{5796}(461, \cdot)$$ n/a 352 2
5796.2.bu $$\chi_{5796}(1609, \cdot)$$ n/a 384 2
5796.2.bz $$\chi_{5796}(2255, \cdot)$$ n/a 1584 2
5796.2.ca $$\chi_{5796}(1471, \cdot)$$ n/a 1728 2
5796.2.cb $$\chi_{5796}(3679, \cdot)$$ n/a 2288 2
5796.2.cc $$\chi_{5796}(2531, \cdot)$$ n/a 2112 2
5796.2.ch $$\chi_{5796}(919, \cdot)$$ n/a 952 2
5796.2.ci $$\chi_{5796}(3635, \cdot)$$ n/a 704 2
5796.2.cj $$\chi_{5796}(3727, \cdot)$$ n/a 880 2
5796.2.ck $$\chi_{5796}(1655, \cdot)$$ n/a 768 2
5796.2.cp $$\chi_{5796}(1931, \cdot)$$ n/a 2288 2
5796.2.cq $$\chi_{5796}(139, \cdot)$$ n/a 2112 2
5796.2.cr $$\chi_{5796}(2623, \cdot)$$ n/a 2112 2
5796.2.cs $$\chi_{5796}(4415, \cdot)$$ n/a 2288 2
5796.2.cx $$\chi_{5796}(4093, \cdot)$$ n/a 384 2
5796.2.cy $$\chi_{5796}(185, \cdot)$$ n/a 352 2
5796.2.cz $$\chi_{5796}(4001, \cdot)$$ n/a 384 2
5796.2.dc $$\chi_{5796}(1513, \cdot)$$ n/a 600 10
5796.2.dd $$\chi_{5796}(701, \cdot)$$ n/a 480 10
5796.2.di $$\chi_{5796}(181, \cdot)$$ n/a 800 10
5796.2.dj $$\chi_{5796}(377, \cdot)$$ n/a 640 10
5796.2.dk $$\chi_{5796}(379, \cdot)$$ n/a 3600 10
5796.2.dl $$\chi_{5796}(71, \cdot)$$ n/a 2880 10
5796.2.dq $$\chi_{5796}(55, \cdot)$$ n/a 4760 10
5796.2.dr $$\chi_{5796}(251, \cdot)$$ n/a 3840 10
5796.2.ds $$\chi_{5796}(193, \cdot)$$ n/a 3840 20
5796.2.dt $$\chi_{5796}(289, \cdot)$$ n/a 1600 20
5796.2.du $$\chi_{5796}(85, \cdot)$$ n/a 2880 20
5796.2.dv $$\chi_{5796}(25, \cdot)$$ n/a 3840 20
5796.2.dy $$\chi_{5796}(65, \cdot)$$ n/a 3840 20
5796.2.dz $$\chi_{5796}(173, \cdot)$$ n/a 3840 20
5796.2.ea $$\chi_{5796}(61, \cdot)$$ n/a 3840 20
5796.2.ef $$\chi_{5796}(227, \cdot)$$ n/a 22880 20
5796.2.eg $$\chi_{5796}(607, \cdot)$$ n/a 22880 20
5796.2.eh $$\chi_{5796}(223, \cdot)$$ n/a 22880 20
5796.2.ei $$\chi_{5796}(83, \cdot)$$ n/a 22880 20
5796.2.en $$\chi_{5796}(143, \cdot)$$ n/a 7680 20
5796.2.eo $$\chi_{5796}(271, \cdot)$$ n/a 9520 20
5796.2.ep $$\chi_{5796}(179, \cdot)$$ n/a 7680 20
5796.2.eq $$\chi_{5796}(235, \cdot)$$ n/a 9520 20
5796.2.ev $$\chi_{5796}(515, \cdot)$$ n/a 22880 20
5796.2.ew $$\chi_{5796}(247, \cdot)$$ n/a 22880 20
5796.2.ex $$\chi_{5796}(43, \cdot)$$ n/a 17280 20
5796.2.ey $$\chi_{5796}(239, \cdot)$$ n/a 17280 20
5796.2.fd $$\chi_{5796}(97, \cdot)$$ n/a 3840 20
5796.2.fe $$\chi_{5796}(41, \cdot)$$ n/a 3840 20
5796.2.ff $$\chi_{5796}(101, \cdot)$$ n/a 3840 20
5796.2.fg $$\chi_{5796}(241, \cdot)$$ n/a 3840 20
5796.2.fl $$\chi_{5796}(269, \cdot)$$ n/a 1280 20
5796.2.fm $$\chi_{5796}(145, \cdot)$$ n/a 1600 20
5796.2.fn $$\chi_{5796}(53, \cdot)$$ n/a 1280 20
5796.2.fs $$\chi_{5796}(113, \cdot)$$ n/a 2880 20
5796.2.ft $$\chi_{5796}(149, \cdot)$$ n/a 3840 20
5796.2.fy $$\chi_{5796}(95, \cdot)$$ n/a 22880 20
5796.2.fz $$\chi_{5796}(67, \cdot)$$ n/a 22880 20
5796.2.ga $$\chi_{5796}(563, \cdot)$$ n/a 22880 20
5796.2.gb $$\chi_{5796}(31, \cdot)$$ n/a 22880 20

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5796))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5796)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(644))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(828))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(966))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1449))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1932))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2898))$$$$^{\oplus 2}$$