## Defining parameters

 Level: $$N$$ = $$6400 = 2^{8} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$44$$ Sturm bound: $$4915200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6400))$$.

Total New Old
Modular forms 1238656 639188 599468
Cusp forms 1218945 634924 584021
Eisenstein series 19711 4264 15447

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6400))$$

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
6400.2.a $$\chi_{6400}(1, \cdot)$$ 6400.2.a.a 1 1
6400.2.a.b 1
6400.2.a.c 1
6400.2.a.d 1
6400.2.a.e 1
6400.2.a.f 1
6400.2.a.g 1
6400.2.a.h 1
6400.2.a.i 1
6400.2.a.j 1
6400.2.a.k 1
6400.2.a.l 1
6400.2.a.m 1
6400.2.a.n 1
6400.2.a.o 1
6400.2.a.p 1
6400.2.a.q 1
6400.2.a.r 1
6400.2.a.s 1
6400.2.a.t 1
6400.2.a.u 1
6400.2.a.v 1
6400.2.a.w 1
6400.2.a.x 1
6400.2.a.y 2
6400.2.a.z 2
6400.2.a.ba 2
6400.2.a.bb 2
6400.2.a.bc 2
6400.2.a.bd 2
6400.2.a.be 2
6400.2.a.bf 2
6400.2.a.bg 2
6400.2.a.bh 2
6400.2.a.bi 2
6400.2.a.bj 2
6400.2.a.bk 2
6400.2.a.bl 2
6400.2.a.bm 2
6400.2.a.bn 2
6400.2.a.bo 2
6400.2.a.bp 2
6400.2.a.bq 2
6400.2.a.br 2
6400.2.a.bs 2
6400.2.a.bt 2
6400.2.a.bu 2
6400.2.a.bv 2
6400.2.a.bw 2
6400.2.a.bx 2
6400.2.a.by 2
6400.2.a.bz 2
6400.2.a.ca 2
6400.2.a.cb 2
6400.2.a.cc 2
6400.2.a.cd 2
6400.2.a.ce 2
6400.2.a.cf 2
6400.2.a.cg 2
6400.2.a.ch 2
6400.2.a.ci 2
6400.2.a.cj 2
6400.2.a.ck 2
6400.2.a.cl 4
6400.2.a.cm 4
6400.2.a.cn 4
6400.2.a.co 4
6400.2.a.cp 4
6400.2.a.cq 4
6400.2.a.cr 4
6400.2.a.cs 4
6400.2.a.ct 4
6400.2.a.cu 4
6400.2.a.cv 4
6400.2.c $$\chi_{6400}(2049, \cdot)$$ n/a 140 1
6400.2.d $$\chi_{6400}(3201, \cdot)$$ n/a 146 1
6400.2.f $$\chi_{6400}(5249, \cdot)$$ n/a 140 1
6400.2.j $$\chi_{6400}(1343, \cdot)$$ n/a 288 2
6400.2.l $$\chi_{6400}(1601, \cdot)$$ n/a 304 2
6400.2.n $$\chi_{6400}(4607, \cdot)$$ n/a 280 2
6400.2.o $$\chi_{6400}(1407, \cdot)$$ n/a 280 2
6400.2.q $$\chi_{6400}(449, \cdot)$$ n/a 288 2
6400.2.s $$\chi_{6400}(4543, \cdot)$$ n/a 288 2
6400.2.u $$\chi_{6400}(1281, \cdot)$$ n/a 944 4
6400.2.v $$\chi_{6400}(543, \cdot)$$ n/a 560 4
6400.2.y $$\chi_{6400}(801, \cdot)$$ n/a 584 4
6400.2.ba $$\chi_{6400}(1249, \cdot)$$ n/a 560 4
6400.2.bb $$\chi_{6400}(2143, \cdot)$$ n/a 560 4
6400.2.be $$\chi_{6400}(129, \cdot)$$ n/a 944 4
6400.2.bg $$\chi_{6400}(769, \cdot)$$ n/a 944 4
6400.2.bj $$\chi_{6400}(641, \cdot)$$ n/a 944 4
6400.2.bl $$\chi_{6400}(143, \cdot)$$ n/a 1136 8
6400.2.bm $$\chi_{6400}(401, \cdot)$$ n/a 1192 8
6400.2.bn $$\chi_{6400}(49, \cdot)$$ n/a 1136 8
6400.2.br $$\chi_{6400}(207, \cdot)$$ n/a 1136 8
6400.2.bt $$\chi_{6400}(703, \cdot)$$ n/a 1920 8
6400.2.bu $$\chi_{6400}(321, \cdot)$$ n/a 1920 8
6400.2.bx $$\chi_{6400}(127, \cdot)$$ n/a 1888 8
6400.2.by $$\chi_{6400}(767, \cdot)$$ n/a 1888 8
6400.2.cb $$\chi_{6400}(1089, \cdot)$$ n/a 1920 8
6400.2.cc $$\chi_{6400}(63, \cdot)$$ n/a 1920 8
6400.2.cf $$\chi_{6400}(7, \cdot)$$ None 0 16
6400.2.cg $$\chi_{6400}(201, \cdot)$$ None 0 16
6400.2.ci $$\chi_{6400}(249, \cdot)$$ None 0 16
6400.2.cl $$\chi_{6400}(407, \cdot)$$ None 0 16
6400.2.cn $$\chi_{6400}(1183, \cdot)$$ n/a 3776 16
6400.2.co $$\chi_{6400}(289, \cdot)$$ n/a 3776 16
6400.2.cq $$\chi_{6400}(161, \cdot)$$ n/a 3776 16
6400.2.ct $$\chi_{6400}(223, \cdot)$$ n/a 3776 16
6400.2.cv $$\chi_{6400}(107, \cdot)$$ n/a 18368 32
6400.2.cx $$\chi_{6400}(101, \cdot)$$ n/a 19360 32
6400.2.cy $$\chi_{6400}(149, \cdot)$$ n/a 18368 32
6400.2.da $$\chi_{6400}(43, \cdot)$$ n/a 18368 32
6400.2.dc $$\chi_{6400}(303, \cdot)$$ n/a 7616 32
6400.2.dg $$\chi_{6400}(209, \cdot)$$ n/a 7616 32
6400.2.dh $$\chi_{6400}(81, \cdot)$$ n/a 7616 32
6400.2.di $$\chi_{6400}(47, \cdot)$$ n/a 7616 32
6400.2.dk $$\chi_{6400}(87, \cdot)$$ None 0 64
6400.2.dn $$\chi_{6400}(9, \cdot)$$ None 0 64
6400.2.dp $$\chi_{6400}(41, \cdot)$$ None 0 64
6400.2.dq $$\chi_{6400}(23, \cdot)$$ None 0 64
6400.2.ds $$\chi_{6400}(67, \cdot)$$ n/a 122624 128
6400.2.du $$\chi_{6400}(29, \cdot)$$ n/a 122624 128
6400.2.dx $$\chi_{6400}(21, \cdot)$$ n/a 122624 128
6400.2.dz $$\chi_{6400}(3, \cdot)$$ n/a 122624 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6400))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6400)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(400))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(640))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(800))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1280))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1600))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3200))$$$$^{\oplus 2}$$