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Properties

Label 5400.2
Level 5400
Weight 2
Dimension 317216
Nonzero newspaces 54
Sturm bound 3110400

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Defining parameters

Level: \( N \) = \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(3110400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5400))\).

Total New Old
Modular forms 787680 319840 467840
Cusp forms 767521 317216 450305
Eisenstein series 20159 2624 17535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5400))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5400.2.a \(\chi_{5400}(1, \cdot)\) 5400.2.a.a 1 1
5400.2.a.b 1
5400.2.a.c 1
5400.2.a.d 1
5400.2.a.e 1
5400.2.a.f 1
5400.2.a.g 1
5400.2.a.h 1
5400.2.a.i 1
5400.2.a.j 1
5400.2.a.k 1
5400.2.a.l 1
5400.2.a.m 1
5400.2.a.n 1
5400.2.a.o 1
5400.2.a.p 1
5400.2.a.q 1
5400.2.a.r 1
5400.2.a.s 1
5400.2.a.t 1
5400.2.a.u 1
5400.2.a.v 1
5400.2.a.w 1
5400.2.a.x 1
5400.2.a.y 1
5400.2.a.z 1
5400.2.a.ba 1
5400.2.a.bb 1
5400.2.a.bc 1
5400.2.a.bd 1
5400.2.a.be 1
5400.2.a.bf 1
5400.2.a.bg 1
5400.2.a.bh 1
5400.2.a.bi 1
5400.2.a.bj 1
5400.2.a.bk 1
5400.2.a.bl 1
5400.2.a.bm 1
5400.2.a.bn 1
5400.2.a.bo 1
5400.2.a.bp 1
5400.2.a.bq 1
5400.2.a.br 1
5400.2.a.bs 1
5400.2.a.bt 1
5400.2.a.bu 1
5400.2.a.bv 1
5400.2.a.bw 2
5400.2.a.bx 2
5400.2.a.by 2
5400.2.a.bz 2
5400.2.a.ca 2
5400.2.a.cb 2
5400.2.a.cc 2
5400.2.a.cd 2
5400.2.a.ce 2
5400.2.a.cf 2
5400.2.a.cg 4
5400.2.a.ch 4
5400.2.b \(\chi_{5400}(2051, \cdot)\) n/a 304 1
5400.2.d \(\chi_{5400}(3349, \cdot)\) n/a 288 1
5400.2.f \(\chi_{5400}(649, \cdot)\) 5400.2.f.a 2 1
5400.2.f.b 2
5400.2.f.c 2
5400.2.f.d 2
5400.2.f.e 2
5400.2.f.f 2
5400.2.f.g 2
5400.2.f.h 2
5400.2.f.i 2
5400.2.f.j 2
5400.2.f.k 2
5400.2.f.l 2
5400.2.f.m 2
5400.2.f.n 2
5400.2.f.o 2
5400.2.f.p 2
5400.2.f.q 2
5400.2.f.r 2
5400.2.f.s 2
5400.2.f.t 2
5400.2.f.u 2
5400.2.f.v 2
5400.2.f.w 2
5400.2.f.x 2
5400.2.f.y 2
5400.2.f.z 2
5400.2.f.ba 2
5400.2.f.bb 2
5400.2.f.bc 4
5400.2.f.bd 4
5400.2.f.be 4
5400.2.f.bf 4
5400.2.h \(\chi_{5400}(4751, \cdot)\) None 0 1
5400.2.k \(\chi_{5400}(2701, \cdot)\) n/a 304 1
5400.2.m \(\chi_{5400}(2699, \cdot)\) n/a 288 1
5400.2.o \(\chi_{5400}(5399, \cdot)\) None 0 1
5400.2.q \(\chi_{5400}(1801, \cdot)\) n/a 114 2
5400.2.s \(\chi_{5400}(593, \cdot)\) n/a 144 2
5400.2.t \(\chi_{5400}(3943, \cdot)\) None 0 2
5400.2.w \(\chi_{5400}(1243, \cdot)\) n/a 576 2
5400.2.x \(\chi_{5400}(3293, \cdot)\) n/a 576 2
5400.2.z \(\chi_{5400}(1081, \cdot)\) n/a 480 4
5400.2.bc \(\chi_{5400}(1799, \cdot)\) None 0 2
5400.2.be \(\chi_{5400}(899, \cdot)\) n/a 424 2
5400.2.bg \(\chi_{5400}(901, \cdot)\) n/a 444 2
5400.2.bh \(\chi_{5400}(1151, \cdot)\) None 0 2
5400.2.bj \(\chi_{5400}(2449, \cdot)\) n/a 108 2
5400.2.bl \(\chi_{5400}(1549, \cdot)\) n/a 424 2
5400.2.bn \(\chi_{5400}(251, \cdot)\) n/a 444 2
5400.2.bp \(\chi_{5400}(601, \cdot)\) n/a 1026 6
5400.2.br \(\chi_{5400}(431, \cdot)\) None 0 4
5400.2.bt \(\chi_{5400}(1729, \cdot)\) n/a 480 4
5400.2.bv \(\chi_{5400}(109, \cdot)\) n/a 1920 4
5400.2.bx \(\chi_{5400}(971, \cdot)\) n/a 1920 4
5400.2.bz \(\chi_{5400}(1079, \cdot)\) None 0 4
5400.2.cb \(\chi_{5400}(539, \cdot)\) n/a 1920 4
5400.2.cd \(\chi_{5400}(541, \cdot)\) n/a 1920 4
5400.2.cf \(\chi_{5400}(307, \cdot)\) n/a 848 4
5400.2.ci \(\chi_{5400}(557, \cdot)\) n/a 848 4
5400.2.cj \(\chi_{5400}(2393, \cdot)\) n/a 216 4
5400.2.cm \(\chi_{5400}(343, \cdot)\) None 0 4
5400.2.cn \(\chi_{5400}(361, \cdot)\) n/a 720 8
5400.2.co \(\chi_{5400}(299, \cdot)\) n/a 3864 6
5400.2.ct \(\chi_{5400}(301, \cdot)\) n/a 4068 6
5400.2.cu \(\chi_{5400}(599, \cdot)\) None 0 6
5400.2.cx \(\chi_{5400}(49, \cdot)\) n/a 972 6
5400.2.cy \(\chi_{5400}(851, \cdot)\) n/a 4068 6
5400.2.cz \(\chi_{5400}(551, \cdot)\) None 0 6
5400.2.da \(\chi_{5400}(349, \cdot)\) n/a 3864 6
5400.2.de \(\chi_{5400}(53, \cdot)\) n/a 3840 8
5400.2.df \(\chi_{5400}(163, \cdot)\) n/a 3840 8
5400.2.di \(\chi_{5400}(487, \cdot)\) None 0 8
5400.2.dj \(\chi_{5400}(377, \cdot)\) n/a 960 8
5400.2.dl \(\chi_{5400}(181, \cdot)\) n/a 2848 8
5400.2.dn \(\chi_{5400}(179, \cdot)\) n/a 2848 8
5400.2.dp \(\chi_{5400}(359, \cdot)\) None 0 8
5400.2.dt \(\chi_{5400}(611, \cdot)\) n/a 2848 8
5400.2.dv \(\chi_{5400}(469, \cdot)\) n/a 2848 8
5400.2.dx \(\chi_{5400}(289, \cdot)\) n/a 720 8
5400.2.dz \(\chi_{5400}(71, \cdot)\) None 0 8
5400.2.ec \(\chi_{5400}(293, \cdot)\) n/a 7728 12
5400.2.ed \(\chi_{5400}(7, \cdot)\) None 0 12
5400.2.eg \(\chi_{5400}(257, \cdot)\) n/a 1944 12
5400.2.eh \(\chi_{5400}(43, \cdot)\) n/a 7728 12
5400.2.ei \(\chi_{5400}(121, \cdot)\) n/a 6480 24
5400.2.ej \(\chi_{5400}(127, \cdot)\) None 0 16
5400.2.em \(\chi_{5400}(17, \cdot)\) n/a 1440 16
5400.2.en \(\chi_{5400}(197, \cdot)\) n/a 5696 16
5400.2.eq \(\chi_{5400}(523, \cdot)\) n/a 5696 16
5400.2.et \(\chi_{5400}(229, \cdot)\) n/a 25824 24
5400.2.eu \(\chi_{5400}(191, \cdot)\) None 0 24
5400.2.ev \(\chi_{5400}(11, \cdot)\) n/a 25824 24
5400.2.ew \(\chi_{5400}(169, \cdot)\) n/a 6480 24
5400.2.ez \(\chi_{5400}(119, \cdot)\) None 0 24
5400.2.fa \(\chi_{5400}(61, \cdot)\) n/a 25824 24
5400.2.ff \(\chi_{5400}(59, \cdot)\) n/a 25824 24
5400.2.fg \(\chi_{5400}(67, \cdot)\) n/a 51648 48
5400.2.fh \(\chi_{5400}(113, \cdot)\) n/a 12960 48
5400.2.fk \(\chi_{5400}(103, \cdot)\) None 0 48
5400.2.fl \(\chi_{5400}(77, \cdot)\) n/a 51648 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2700))\)\(^{\oplus 2}\)