# Properties

 Label 5445.2 Level 5445 Weight 2 Dimension 742389 Nonzero newspaces 48 Sturm bound 4181760

## Defining parameters

 Level: $$N$$ = $$5445 = 3^{2} \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$4181760$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5445))$$.

Total New Old
Modular forms 1055680 749975 305705
Cusp forms 1035201 742389 292812
Eisenstein series 20479 7586 12893

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5445))$$

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
5445.2.a $$\chi_{5445}(1, \cdot)$$ 5445.2.a.a 1 1
5445.2.a.b 1
5445.2.a.c 1
5445.2.a.d 1
5445.2.a.e 1
5445.2.a.f 1
5445.2.a.g 1
5445.2.a.h 1
5445.2.a.i 1
5445.2.a.j 1
5445.2.a.k 1
5445.2.a.l 1
5445.2.a.m 2
5445.2.a.n 2
5445.2.a.o 2
5445.2.a.p 2
5445.2.a.q 2
5445.2.a.r 2
5445.2.a.s 2
5445.2.a.t 2
5445.2.a.u 2
5445.2.a.v 2
5445.2.a.w 2
5445.2.a.x 2
5445.2.a.y 2
5445.2.a.z 3
5445.2.a.ba 3
5445.2.a.bb 3
5445.2.a.bc 3
5445.2.a.bd 3
5445.2.a.be 4
5445.2.a.bf 4
5445.2.a.bg 4
5445.2.a.bh 4
5445.2.a.bi 4
5445.2.a.bj 4
5445.2.a.bk 4
5445.2.a.bl 4
5445.2.a.bm 4
5445.2.a.bn 4
5445.2.a.bo 4
5445.2.a.bp 4
5445.2.a.bq 4
5445.2.a.br 4
5445.2.a.bs 4
5445.2.a.bt 4
5445.2.a.bu 4
5445.2.a.bv 4
5445.2.a.bw 6
5445.2.a.bx 6
5445.2.a.by 6
5445.2.a.bz 6
5445.2.a.ca 8
5445.2.a.cb 8
5445.2.a.cc 8
5445.2.a.cd 8
5445.2.c $$\chi_{5445}(2179, \cdot)$$ n/a 264 1
5445.2.d $$\chi_{5445}(5444, \cdot)$$ n/a 216 1
5445.2.f $$\chi_{5445}(3266, \cdot)$$ n/a 144 1
5445.2.i $$\chi_{5445}(1816, \cdot)$$ n/a 872 2
5445.2.k $$\chi_{5445}(1693, \cdot)$$ n/a 524 2
5445.2.l $$\chi_{5445}(2663, \cdot)$$ n/a 436 2
5445.2.n $$\chi_{5445}(856, \cdot)$$ n/a 720 4
5445.2.p $$\chi_{5445}(1451, \cdot)$$ n/a 864 2
5445.2.r $$\chi_{5445}(1814, \cdot)$$ n/a 1264 2
5445.2.u $$\chi_{5445}(364, \cdot)$$ n/a 1272 2
5445.2.x $$\chi_{5445}(161, \cdot)$$ n/a 576 4
5445.2.z $$\chi_{5445}(1304, \cdot)$$ n/a 864 4
5445.2.ba $$\chi_{5445}(874, \cdot)$$ n/a 1048 4
5445.2.bc $$\chi_{5445}(496, \cdot)$$ n/a 2200 10
5445.2.bd $$\chi_{5445}(122, \cdot)$$ n/a 2544 4
5445.2.bg $$\chi_{5445}(967, \cdot)$$ n/a 2528 4
5445.2.bh $$\chi_{5445}(511, \cdot)$$ n/a 3456 8
5445.2.bj $$\chi_{5445}(323, \cdot)$$ n/a 1728 8
5445.2.bk $$\chi_{5445}(118, \cdot)$$ n/a 2096 8
5445.2.bo $$\chi_{5445}(296, \cdot)$$ n/a 1760 10
5445.2.bq $$\chi_{5445}(494, \cdot)$$ n/a 2640 10
5445.2.br $$\chi_{5445}(199, \cdot)$$ n/a 3280 10
5445.2.bt $$\chi_{5445}(124, \cdot)$$ n/a 5056 8
5445.2.bw $$\chi_{5445}(239, \cdot)$$ n/a 5056 8
5445.2.by $$\chi_{5445}(596, \cdot)$$ n/a 3456 8
5445.2.ca $$\chi_{5445}(166, \cdot)$$ n/a 10560 20
5445.2.cc $$\chi_{5445}(188, \cdot)$$ n/a 5280 20
5445.2.cd $$\chi_{5445}(208, \cdot)$$ n/a 6560 20
5445.2.cf $$\chi_{5445}(91, \cdot)$$ n/a 8800 40
5445.2.cg $$\chi_{5445}(112, \cdot)$$ n/a 10112 16
5445.2.cj $$\chi_{5445}(608, \cdot)$$ n/a 10112 16
5445.2.ck $$\chi_{5445}(34, \cdot)$$ n/a 15760 20
5445.2.cn $$\chi_{5445}(164, \cdot)$$ n/a 15760 20
5445.2.cp $$\chi_{5445}(131, \cdot)$$ n/a 10560 20
5445.2.cs $$\chi_{5445}(64, \cdot)$$ n/a 13120 40
5445.2.ct $$\chi_{5445}(134, \cdot)$$ n/a 10560 40
5445.2.cv $$\chi_{5445}(116, \cdot)$$ n/a 7040 40
5445.2.cy $$\chi_{5445}(43, \cdot)$$ n/a 31520 40
5445.2.db $$\chi_{5445}(23, \cdot)$$ n/a 31520 40
5445.2.dc $$\chi_{5445}(16, \cdot)$$ n/a 42240 80
5445.2.de $$\chi_{5445}(28, \cdot)$$ n/a 26240 80
5445.2.df $$\chi_{5445}(53, \cdot)$$ n/a 21120 80
5445.2.di $$\chi_{5445}(41, \cdot)$$ n/a 42240 80
5445.2.dk $$\chi_{5445}(29, \cdot)$$ n/a 63040 80
5445.2.dn $$\chi_{5445}(4, \cdot)$$ n/a 63040 80
5445.2.do $$\chi_{5445}(38, \cdot)$$ n/a 126080 160
5445.2.dr $$\chi_{5445}(7, \cdot)$$ n/a 126080 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5445))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5445)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(495))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(605))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1089))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1815))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5445))$$$$^{\oplus 1}$$