Properties

Label 6400.2
Level 6400
Weight 2
Dimension 634924
Nonzero newspaces 44
Sturm bound 4915200

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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

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