# Properties

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

## 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(5400)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 27}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(600))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(675))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(900))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1350))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1800))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2700))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5400))$$$$^{\oplus 1}$$