## Defining parameters

 Level: $$N$$ = $$5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$3283200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5550))$$.

Total New Old
Modular forms 828864 188852 640012
Cusp forms 812737 188852 623885
Eisenstein series 16127 0 16127

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5550))$$

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
5550.2.a $$\chi_{5550}(1, \cdot)$$ 5550.2.a.a 1 1
5550.2.a.b 1
5550.2.a.c 1
5550.2.a.d 1
5550.2.a.e 1
5550.2.a.f 1
5550.2.a.g 1
5550.2.a.h 1
5550.2.a.i 1
5550.2.a.j 1
5550.2.a.k 1
5550.2.a.l 1
5550.2.a.m 1
5550.2.a.n 1
5550.2.a.o 1
5550.2.a.p 1
5550.2.a.q 1
5550.2.a.r 1
5550.2.a.s 1
5550.2.a.t 1
5550.2.a.u 1
5550.2.a.v 1
5550.2.a.w 1
5550.2.a.x 1
5550.2.a.y 1
5550.2.a.z 1
5550.2.a.ba 1
5550.2.a.bb 1
5550.2.a.bc 1
5550.2.a.bd 1
5550.2.a.be 1
5550.2.a.bf 1
5550.2.a.bg 1
5550.2.a.bh 1
5550.2.a.bi 1
5550.2.a.bj 1
5550.2.a.bk 1
5550.2.a.bl 1
5550.2.a.bm 1
5550.2.a.bn 1
5550.2.a.bo 1
5550.2.a.bp 1
5550.2.a.bq 1
5550.2.a.br 1
5550.2.a.bs 2
5550.2.a.bt 2
5550.2.a.bu 2
5550.2.a.bv 2
5550.2.a.bw 2
5550.2.a.bx 2
5550.2.a.by 2
5550.2.a.bz 2
5550.2.a.ca 2
5550.2.a.cb 2
5550.2.a.cc 2
5550.2.a.cd 3
5550.2.a.ce 3
5550.2.a.cf 3
5550.2.a.cg 3
5550.2.a.ch 3
5550.2.a.ci 3
5550.2.a.cj 4
5550.2.a.ck 4
5550.2.a.cl 4
5550.2.a.cm 4
5550.2.a.cn 4
5550.2.a.co 5
5550.2.a.cp 5
5550.2.d $$\chi_{5550}(1999, \cdot)$$ n/a 108 1
5550.2.e $$\chi_{5550}(1849, \cdot)$$ n/a 116 1
5550.2.h $$\chi_{5550}(5401, \cdot)$$ n/a 118 1
5550.2.i $$\chi_{5550}(3451, \cdot)$$ n/a 240 2
5550.2.k $$\chi_{5550}(2399, \cdot)$$ n/a 456 2
5550.2.l $$\chi_{5550}(43, \cdot)$$ n/a 228 2
5550.2.m $$\chi_{5550}(593, \cdot)$$ n/a 432 2
5550.2.n $$\chi_{5550}(443, \cdot)$$ n/a 456 2
5550.2.o $$\chi_{5550}(2707, \cdot)$$ n/a 228 2
5550.2.u $$\chi_{5550}(401, \cdot)$$ n/a 484 2
5550.2.v $$\chi_{5550}(1111, \cdot)$$ n/a 720 4
5550.2.y $$\chi_{5550}(751, \cdot)$$ n/a 236 2
5550.2.bb $$\chi_{5550}(2749, \cdot)$$ n/a 232 2
5550.2.bc $$\chi_{5550}(1099, \cdot)$$ n/a 224 2
5550.2.bd $$\chi_{5550}(451, \cdot)$$ n/a 732 6
5550.2.be $$\chi_{5550}(739, \cdot)$$ n/a 752 4
5550.2.bf $$\chi_{5550}(889, \cdot)$$ n/a 720 4
5550.2.bi $$\chi_{5550}(961, \cdot)$$ n/a 768 4
5550.2.bm $$\chi_{5550}(251, \cdot)$$ n/a 968 4
5550.2.bn $$\chi_{5550}(643, \cdot)$$ n/a 456 4
5550.2.bo $$\chi_{5550}(1343, \cdot)$$ n/a 912 4
5550.2.bp $$\chi_{5550}(1157, \cdot)$$ n/a 912 4
5550.2.bq $$\chi_{5550}(193, \cdot)$$ n/a 456 4
5550.2.bw $$\chi_{5550}(1799, \cdot)$$ n/a 912 4
5550.2.bx $$\chi_{5550}(121, \cdot)$$ n/a 1504 8
5550.2.by $$\chi_{5550}(1249, \cdot)$$ n/a 696 6
5550.2.bz $$\chi_{5550}(49, \cdot)$$ n/a 672 6
5550.2.ca $$\chi_{5550}(151, \cdot)$$ n/a 720 6
5550.2.cf $$\chi_{5550}(179, \cdot)$$ n/a 3040 8
5550.2.cl $$\chi_{5550}(253, \cdot)$$ n/a 1520 8
5550.2.cm $$\chi_{5550}(887, \cdot)$$ n/a 3040 8
5550.2.cn $$\chi_{5550}(1037, \cdot)$$ n/a 2880 8
5550.2.co $$\chi_{5550}(697, \cdot)$$ n/a 1520 8
5550.2.cp $$\chi_{5550}(191, \cdot)$$ n/a 3040 8
5550.2.cr $$\chi_{5550}(841, \cdot)$$ n/a 1536 8
5550.2.cu $$\chi_{5550}(1009, \cdot)$$ n/a 1536 8
5550.2.cv $$\chi_{5550}(529, \cdot)$$ n/a 1504 8
5550.2.da $$\chi_{5550}(449, \cdot)$$ n/a 2736 12
5550.2.db $$\chi_{5550}(701, \cdot)$$ n/a 2880 12
5550.2.de $$\chi_{5550}(457, \cdot)$$ n/a 1368 12
5550.2.df $$\chi_{5550}(107, \cdot)$$ n/a 2736 12
5550.2.di $$\chi_{5550}(707, \cdot)$$ n/a 2736 12
5550.2.dj $$\chi_{5550}(607, \cdot)$$ n/a 1368 12
5550.2.dk $$\chi_{5550}(181, \cdot)$$ n/a 4512 24
5550.2.dl $$\chi_{5550}(341, \cdot)$$ n/a 6080 16
5550.2.dr $$\chi_{5550}(547, \cdot)$$ n/a 3040 16
5550.2.ds $$\chi_{5550}(47, \cdot)$$ n/a 6080 16
5550.2.dt $$\chi_{5550}(233, \cdot)$$ n/a 6080 16
5550.2.du $$\chi_{5550}(97, \cdot)$$ n/a 3040 16
5550.2.dv $$\chi_{5550}(29, \cdot)$$ n/a 6080 16
5550.2.eb $$\chi_{5550}(361, \cdot)$$ n/a 4608 24
5550.2.ec $$\chi_{5550}(229, \cdot)$$ n/a 4608 24
5550.2.ed $$\chi_{5550}(139, \cdot)$$ n/a 4512 24
5550.2.ee $$\chi_{5550}(13, \cdot)$$ n/a 9120 48
5550.2.ef $$\chi_{5550}(77, \cdot)$$ n/a 18240 48
5550.2.ei $$\chi_{5550}(53, \cdot)$$ n/a 18240 48
5550.2.ej $$\chi_{5550}(163, \cdot)$$ n/a 9120 48
5550.2.em $$\chi_{5550}(131, \cdot)$$ n/a 18240 48
5550.2.en $$\chi_{5550}(59, \cdot)$$ n/a 18240 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5550))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5550)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(111))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(222))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(370))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(555))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(925))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1110))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1850))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2775))$$$$^{\oplus 2}$$