# Properties

 Label 5700.2 Level 5700 Weight 2 Dimension 345062 Nonzero newspaces 72 Sturm bound 3456000

# Learn more

## Defining parameters

 Level: $$N$$ = $$5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$3456000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5700))$$.

Total New Old
Modular forms 874080 347846 526234
Cusp forms 853921 345062 508859
Eisenstein series 20159 2784 17375

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5700))$$

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
5700.2.a $$\chi_{5700}(1, \cdot)$$ 5700.2.a.a 1 1
5700.2.a.b 1
5700.2.a.c 1
5700.2.a.d 1
5700.2.a.e 1
5700.2.a.f 1
5700.2.a.g 1
5700.2.a.h 1
5700.2.a.i 1
5700.2.a.j 1
5700.2.a.k 1
5700.2.a.l 1
5700.2.a.m 1
5700.2.a.n 1
5700.2.a.o 1
5700.2.a.p 1
5700.2.a.q 1
5700.2.a.r 1
5700.2.a.s 2
5700.2.a.t 2
5700.2.a.u 2
5700.2.a.v 2
5700.2.a.w 3
5700.2.a.x 3
5700.2.a.y 3
5700.2.a.z 3
5700.2.a.ba 4
5700.2.a.bb 4
5700.2.a.bc 5
5700.2.a.bd 5
5700.2.b $$\chi_{5700}(151, \cdot)$$ n/a 380 1
5700.2.e $$\chi_{5700}(2849, \cdot)$$ n/a 120 1
5700.2.f $$\chi_{5700}(3649, \cdot)$$ 5700.2.f.a 2 1
5700.2.f.b 2
5700.2.f.c 2
5700.2.f.d 2
5700.2.f.e 2
5700.2.f.f 2
5700.2.f.g 2
5700.2.f.h 2
5700.2.f.i 2
5700.2.f.j 2
5700.2.f.k 2
5700.2.f.l 2
5700.2.f.m 4
5700.2.f.n 4
5700.2.f.o 4
5700.2.f.p 6
5700.2.f.q 6
5700.2.f.r 8
5700.2.i $$\chi_{5700}(4751, \cdot)$$ n/a 684 1
5700.2.j $$\chi_{5700}(4901, \cdot)$$ n/a 126 1
5700.2.m $$\chi_{5700}(3799, \cdot)$$ n/a 360 1
5700.2.n $$\chi_{5700}(2699, \cdot)$$ n/a 648 1
5700.2.q $$\chi_{5700}(2101, \cdot)$$ n/a 128 2
5700.2.s $$\chi_{5700}(343, \cdot)$$ n/a 648 2
5700.2.u $$\chi_{5700}(2357, \cdot)$$ n/a 216 2
5700.2.w $$\chi_{5700}(2507, \cdot)$$ n/a 1424 2
5700.2.y $$\chi_{5700}(493, \cdot)$$ n/a 120 2
5700.2.z $$\chi_{5700}(1141, \cdot)$$ n/a 368 4
5700.2.ba $$\chi_{5700}(449, \cdot)$$ n/a 240 2
5700.2.bd $$\chi_{5700}(3451, \cdot)$$ n/a 760 2
5700.2.be $$\chi_{5700}(1151, \cdot)$$ n/a 1496 2
5700.2.bh $$\chi_{5700}(49, \cdot)$$ n/a 120 2
5700.2.bi $$\chi_{5700}(1399, \cdot)$$ n/a 720 2
5700.2.bl $$\chi_{5700}(2501, \cdot)$$ n/a 252 2
5700.2.bo $$\chi_{5700}(4799, \cdot)$$ n/a 1424 2
5700.2.bp $$\chi_{5700}(301, \cdot)$$ n/a 378 6
5700.2.bq $$\chi_{5700}(191, \cdot)$$ n/a 4320 4
5700.2.bt $$\chi_{5700}(229, \cdot)$$ n/a 352 4
5700.2.bu $$\chi_{5700}(569, \cdot)$$ n/a 800 4
5700.2.bx $$\chi_{5700}(1291, \cdot)$$ n/a 2400 4
5700.2.ca $$\chi_{5700}(419, \cdot)$$ n/a 4320 4
5700.2.cb $$\chi_{5700}(379, \cdot)$$ n/a 2400 4
5700.2.ce $$\chi_{5700}(341, \cdot)$$ n/a 800 4
5700.2.cf $$\chi_{5700}(1493, \cdot)$$ n/a 480 4
5700.2.ch $$\chi_{5700}(7, \cdot)$$ n/a 1440 4
5700.2.cj $$\chi_{5700}(1057, \cdot)$$ n/a 240 4
5700.2.cl $$\chi_{5700}(107, \cdot)$$ n/a 2848 4
5700.2.cn $$\chi_{5700}(121, \cdot)$$ n/a 800 8
5700.2.cq $$\chi_{5700}(899, \cdot)$$ n/a 4272 6
5700.2.cr $$\chi_{5700}(2599, \cdot)$$ n/a 2160 6
5700.2.cu $$\chi_{5700}(401, \cdot)$$ n/a 762 6
5700.2.cw $$\chi_{5700}(1849, \cdot)$$ n/a 360 6
5700.2.cx $$\chi_{5700}(251, \cdot)$$ n/a 4488 6
5700.2.da $$\chi_{5700}(451, \cdot)$$ n/a 2280 6
5700.2.db $$\chi_{5700}(1649, \cdot)$$ n/a 720 6
5700.2.dd $$\chi_{5700}(37, \cdot)$$ n/a 800 8
5700.2.df $$\chi_{5700}(227, \cdot)$$ n/a 9536 8
5700.2.dh $$\chi_{5700}(77, \cdot)$$ n/a 1440 8
5700.2.dj $$\chi_{5700}(1027, \cdot)$$ n/a 4320 8
5700.2.dl $$\chi_{5700}(1189, \cdot)$$ n/a 800 8
5700.2.do $$\chi_{5700}(11, \cdot)$$ n/a 9536 8
5700.2.dp $$\chi_{5700}(31, \cdot)$$ n/a 4800 8
5700.2.ds $$\chi_{5700}(1589, \cdot)$$ n/a 1600 8
5700.2.dt $$\chi_{5700}(239, \cdot)$$ n/a 9536 8
5700.2.dw $$\chi_{5700}(221, \cdot)$$ n/a 1600 8
5700.2.dz $$\chi_{5700}(259, \cdot)$$ n/a 4800 8
5700.2.ea $$\chi_{5700}(143, \cdot)$$ n/a 8544 12
5700.2.ec $$\chi_{5700}(193, \cdot)$$ n/a 720 12
5700.2.ee $$\chi_{5700}(557, \cdot)$$ n/a 1440 12
5700.2.eg $$\chi_{5700}(43, \cdot)$$ n/a 4320 12
5700.2.ei $$\chi_{5700}(61, \cdot)$$ n/a 2400 24
5700.2.ek $$\chi_{5700}(563, \cdot)$$ n/a 19072 16
5700.2.em $$\chi_{5700}(217, \cdot)$$ n/a 1600 16
5700.2.eo $$\chi_{5700}(163, \cdot)$$ n/a 9600 16
5700.2.eq $$\chi_{5700}(197, \cdot)$$ n/a 3200 16
5700.2.er $$\chi_{5700}(41, \cdot)$$ n/a 4800 24
5700.2.eu $$\chi_{5700}(79, \cdot)$$ n/a 14400 24
5700.2.ev $$\chi_{5700}(119, \cdot)$$ n/a 28608 24
5700.2.ez $$\chi_{5700}(29, \cdot)$$ n/a 4800 24
5700.2.fa $$\chi_{5700}(91, \cdot)$$ n/a 14400 24
5700.2.fd $$\chi_{5700}(131, \cdot)$$ n/a 28608 24
5700.2.fe $$\chi_{5700}(169, \cdot)$$ n/a 2400 24
5700.2.fh $$\chi_{5700}(187, \cdot)$$ n/a 28800 48
5700.2.fj $$\chi_{5700}(17, \cdot)$$ n/a 9600 48
5700.2.fl $$\chi_{5700}(13, \cdot)$$ n/a 4800 48
5700.2.fn $$\chi_{5700}(167, \cdot)$$ n/a 57216 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5700))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5700)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(950))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1140))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1425))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1900))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2850))$$$$^{\oplus 2}$$