Properties

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

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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

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