# Properties

 Label 4851.2 Level 4851 Weight 2 Dimension 628596 Nonzero newspaces 80 Sturm bound 3386880

## Defining parameters

 Level: $$N$$ = $$4851 = 3^{2} \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$3386880$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4851))$$.

Total New Old
Modular forms 856320 636452 219868
Cusp forms 837121 628596 208525
Eisenstein series 19199 7856 11343

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4851))$$

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
4851.2.a $$\chi_{4851}(1, \cdot)$$ 4851.2.a.a 1 1
4851.2.a.b 1
4851.2.a.c 1
4851.2.a.d 1
4851.2.a.e 1
4851.2.a.f 1
4851.2.a.g 1
4851.2.a.h 1
4851.2.a.i 1
4851.2.a.j 1
4851.2.a.k 1
4851.2.a.l 1
4851.2.a.m 1
4851.2.a.n 1
4851.2.a.o 1
4851.2.a.p 1
4851.2.a.q 1
4851.2.a.r 1
4851.2.a.s 1
4851.2.a.t 1
4851.2.a.u 2
4851.2.a.v 2
4851.2.a.w 2
4851.2.a.x 2
4851.2.a.y 2
4851.2.a.z 2
4851.2.a.ba 2
4851.2.a.bb 2
4851.2.a.bc 2
4851.2.a.bd 2
4851.2.a.be 2
4851.2.a.bf 2
4851.2.a.bg 2
4851.2.a.bh 2
4851.2.a.bi 3
4851.2.a.bj 3
4851.2.a.bk 3
4851.2.a.bl 3
4851.2.a.bm 3
4851.2.a.bn 3
4851.2.a.bo 3
4851.2.a.bp 3
4851.2.a.bq 4
4851.2.a.br 4
4851.2.a.bs 4
4851.2.a.bt 4
4851.2.a.bu 4
4851.2.a.bv 4
4851.2.a.bw 4
4851.2.a.bx 4
4851.2.a.by 4
4851.2.a.bz 5
4851.2.a.ca 5
4851.2.a.cb 6
4851.2.a.cc 6
4851.2.a.cd 6
4851.2.a.ce 6
4851.2.a.cf 10
4851.2.a.cg 10
4851.2.a.ch 10
4851.2.c $$\chi_{4851}(3772, \cdot)$$ n/a 196 1
4851.2.e $$\chi_{4851}(881, \cdot)$$ n/a 136 1
4851.2.g $$\chi_{4851}(197, \cdot)$$ n/a 164 1
4851.2.i $$\chi_{4851}(1684, \cdot)$$ n/a 332 2
4851.2.j $$\chi_{4851}(1618, \cdot)$$ n/a 820 2
4851.2.k $$\chi_{4851}(67, \cdot)$$ n/a 800 2
4851.2.l $$\chi_{4851}(1255, \cdot)$$ n/a 800 2
4851.2.m $$\chi_{4851}(883, \cdot)$$ n/a 800 4
4851.2.n $$\chi_{4851}(2432, \cdot)$$ n/a 800 2
4851.2.p $$\chi_{4851}(3706, \cdot)$$ n/a 944 2
4851.2.r $$\chi_{4851}(1451, \cdot)$$ n/a 944 2
4851.2.w $$\chi_{4851}(1814, \cdot)$$ n/a 964 2
4851.2.x $$\chi_{4851}(1880, \cdot)$$ n/a 320 2
4851.2.ba $$\chi_{4851}(472, \cdot)$$ n/a 944 2
4851.2.bd $$\chi_{4851}(2498, \cdot)$$ n/a 800 2
4851.2.be $$\chi_{4851}(2861, \cdot)$$ n/a 264 2
4851.2.bg $$\chi_{4851}(901, \cdot)$$ n/a 392 2
4851.2.bj $$\chi_{4851}(538, \cdot)$$ n/a 944 2
4851.2.bk $$\chi_{4851}(815, \cdot)$$ n/a 800 2
4851.2.bn $$\chi_{4851}(263, \cdot)$$ n/a 944 2
4851.2.bp $$\chi_{4851}(694, \cdot)$$ n/a 1392 6
4851.2.br $$\chi_{4851}(1520, \cdot)$$ n/a 656 4
4851.2.bt $$\chi_{4851}(1763, \cdot)$$ n/a 640 4
4851.2.bv $$\chi_{4851}(244, \cdot)$$ n/a 784 4
4851.2.by $$\chi_{4851}(890, \cdot)$$ n/a 1344 6
4851.2.ca $$\chi_{4851}(188, \cdot)$$ n/a 1104 6
4851.2.cc $$\chi_{4851}(307, \cdot)$$ n/a 1668 6
4851.2.ce $$\chi_{4851}(214, \cdot)$$ n/a 3776 8
4851.2.cf $$\chi_{4851}(520, \cdot)$$ n/a 3776 8
4851.2.cg $$\chi_{4851}(361, \cdot)$$ n/a 1568 8
4851.2.ch $$\chi_{4851}(148, \cdot)$$ n/a 3856 8
4851.2.ci $$\chi_{4851}(529, \cdot)$$ n/a 6720 12
4851.2.cj $$\chi_{4851}(331, \cdot)$$ n/a 6720 12
4851.2.ck $$\chi_{4851}(232, \cdot)$$ n/a 6720 12
4851.2.cl $$\chi_{4851}(100, \cdot)$$ n/a 2808 12
4851.2.cn $$\chi_{4851}(1157, \cdot)$$ n/a 3776 8
4851.2.cq $$\chi_{4851}(1697, \cdot)$$ n/a 3776 8
4851.2.cs $$\chi_{4851}(19, \cdot)$$ n/a 1568 8
4851.2.ct $$\chi_{4851}(391, \cdot)$$ n/a 3776 8
4851.2.cv $$\chi_{4851}(146, \cdot)$$ n/a 3776 8
4851.2.cy $$\chi_{4851}(80, \cdot)$$ n/a 1280 8
4851.2.da $$\chi_{4851}(754, \cdot)$$ n/a 3776 8
4851.2.dc $$\chi_{4851}(50, \cdot)$$ n/a 3856 8
4851.2.df $$\chi_{4851}(116, \cdot)$$ n/a 1280 8
4851.2.dj $$\chi_{4851}(128, \cdot)$$ n/a 3776 8
4851.2.dl $$\chi_{4851}(178, \cdot)$$ n/a 3776 8
4851.2.dn $$\chi_{4851}(509, \cdot)$$ n/a 3776 8
4851.2.do $$\chi_{4851}(64, \cdot)$$ n/a 6672 24
4851.2.dq $$\chi_{4851}(527, \cdot)$$ n/a 8016 12
4851.2.dt $$\chi_{4851}(122, \cdot)$$ n/a 6720 12
4851.2.du $$\chi_{4851}(76, \cdot)$$ n/a 8016 12
4851.2.dx $$\chi_{4851}(10, \cdot)$$ n/a 3336 12
4851.2.dz $$\chi_{4851}(89, \cdot)$$ n/a 2256 12
4851.2.ea $$\chi_{4851}(419, \cdot)$$ n/a 6720 12
4851.2.ed $$\chi_{4851}(439, \cdot)$$ n/a 8016 12
4851.2.eg $$\chi_{4851}(296, \cdot)$$ n/a 2688 12
4851.2.eh $$\chi_{4851}(428, \cdot)$$ n/a 8016 12
4851.2.em $$\chi_{4851}(32, \cdot)$$ n/a 8016 12
4851.2.eo $$\chi_{4851}(241, \cdot)$$ n/a 8016 12
4851.2.eq $$\chi_{4851}(320, \cdot)$$ n/a 6720 12
4851.2.es $$\chi_{4851}(118, \cdot)$$ n/a 6672 24
4851.2.eu $$\chi_{4851}(125, \cdot)$$ n/a 5376 24
4851.2.ew $$\chi_{4851}(8, \cdot)$$ n/a 5376 24
4851.2.ey $$\chi_{4851}(169, \cdot)$$ n/a 32064 48
4851.2.ez $$\chi_{4851}(37, \cdot)$$ n/a 13344 48
4851.2.fa $$\chi_{4851}(4, \cdot)$$ n/a 32064 48
4851.2.fb $$\chi_{4851}(25, \cdot)$$ n/a 32064 48
4851.2.fc $$\chi_{4851}(5, \cdot)$$ n/a 32064 48
4851.2.fe $$\chi_{4851}(40, \cdot)$$ n/a 32064 48
4851.2.fg $$\chi_{4851}(2, \cdot)$$ n/a 32064 48
4851.2.fk $$\chi_{4851}(107, \cdot)$$ n/a 10752 48
4851.2.fn $$\chi_{4851}(29, \cdot)$$ n/a 32064 48
4851.2.fp $$\chi_{4851}(61, \cdot)$$ n/a 32064 48
4851.2.fr $$\chi_{4851}(26, \cdot)$$ n/a 10752 48
4851.2.fu $$\chi_{4851}(20, \cdot)$$ n/a 32064 48
4851.2.fw $$\chi_{4851}(13, \cdot)$$ n/a 32064 48
4851.2.fx $$\chi_{4851}(73, \cdot)$$ n/a 13344 48
4851.2.fz $$\chi_{4851}(47, \cdot)$$ n/a 32064 48
4851.2.gc $$\chi_{4851}(74, \cdot)$$ n/a 32064 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4851))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4851)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(693))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1617))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4851))$$$$^{\oplus 1}$$