## Defining parameters

 Level: $$N$$ = $$4900 = 2^{2} \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$2822400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4900))$$.

Total New Old
Modular forms 714000 366023 347977
Cusp forms 697201 362047 335154
Eisenstein series 16799 3976 12823

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4900))$$

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
4900.2.a $$\chi_{4900}(1, \cdot)$$ 4900.2.a.a 1 1
4900.2.a.b 1
4900.2.a.c 1
4900.2.a.d 1
4900.2.a.e 1
4900.2.a.f 1
4900.2.a.g 1
4900.2.a.h 1
4900.2.a.i 1
4900.2.a.j 1
4900.2.a.k 1
4900.2.a.l 1
4900.2.a.m 1
4900.2.a.n 1
4900.2.a.o 1
4900.2.a.p 1
4900.2.a.q 1
4900.2.a.r 1
4900.2.a.s 1
4900.2.a.t 1
4900.2.a.u 1
4900.2.a.v 1
4900.2.a.w 1
4900.2.a.x 2
4900.2.a.y 2
4900.2.a.z 2
4900.2.a.ba 3
4900.2.a.bb 3
4900.2.a.bc 3
4900.2.a.bd 3
4900.2.a.be 4
4900.2.a.bf 4
4900.2.a.bg 4
4900.2.a.bh 4
4900.2.a.bi 4
4900.2.a.bj 4
4900.2.c $$\chi_{4900}(4899, \cdot)$$ n/a 352 1
4900.2.e $$\chi_{4900}(2549, \cdot)$$ 4900.2.e.a 2 1
4900.2.e.b 2
4900.2.e.c 2
4900.2.e.d 2
4900.2.e.e 2
4900.2.e.f 2
4900.2.e.g 2
4900.2.e.h 2
4900.2.e.i 2
4900.2.e.j 2
4900.2.e.k 2
4900.2.e.l 2
4900.2.e.m 2
4900.2.e.n 2
4900.2.e.o 2
4900.2.e.p 4
4900.2.e.q 4
4900.2.e.r 4
4900.2.e.s 6
4900.2.e.t 6
4900.2.e.u 8
4900.2.g $$\chi_{4900}(2351, \cdot)$$ n/a 368 1
4900.2.i $$\chi_{4900}(3301, \cdot)$$ n/a 126 2
4900.2.k $$\chi_{4900}(2843, \cdot)$$ n/a 718 2
4900.2.m $$\chi_{4900}(293, \cdot)$$ n/a 120 2
4900.2.n $$\chi_{4900}(981, \cdot)$$ n/a 412 4
4900.2.p $$\chi_{4900}(3351, \cdot)$$ n/a 736 2
4900.2.r $$\chi_{4900}(949, \cdot)$$ n/a 120 2
4900.2.t $$\chi_{4900}(999, \cdot)$$ n/a 704 2
4900.2.v $$\chi_{4900}(701, \cdot)$$ n/a 528 6
4900.2.x $$\chi_{4900}(391, \cdot)$$ n/a 2368 4
4900.2.z $$\chi_{4900}(589, \cdot)$$ n/a 408 4
4900.2.bb $$\chi_{4900}(979, \cdot)$$ n/a 2368 4
4900.2.bd $$\chi_{4900}(1293, \cdot)$$ n/a 240 4
4900.2.bf $$\chi_{4900}(1243, \cdot)$$ n/a 1408 4
4900.2.bj $$\chi_{4900}(251, \cdot)$$ n/a 3156 6
4900.2.bl $$\chi_{4900}(449, \cdot)$$ n/a 504 6
4900.2.bn $$\chi_{4900}(699, \cdot)$$ n/a 3000 6
4900.2.bo $$\chi_{4900}(361, \cdot)$$ n/a 800 8
4900.2.bp $$\chi_{4900}(97, \cdot)$$ n/a 800 8
4900.2.br $$\chi_{4900}(687, \cdot)$$ n/a 4840 8
4900.2.bt $$\chi_{4900}(401, \cdot)$$ n/a 1068 12
4900.2.bv $$\chi_{4900}(657, \cdot)$$ n/a 1008 12
4900.2.bx $$\chi_{4900}(43, \cdot)$$ n/a 6000 12
4900.2.bz $$\chi_{4900}(19, \cdot)$$ n/a 4736 8
4900.2.cb $$\chi_{4900}(569, \cdot)$$ n/a 800 8
4900.2.cd $$\chi_{4900}(31, \cdot)$$ n/a 4736 8
4900.2.cf $$\chi_{4900}(141, \cdot)$$ n/a 3360 24
4900.2.cg $$\chi_{4900}(199, \cdot)$$ n/a 6000 12
4900.2.ci $$\chi_{4900}(149, \cdot)$$ n/a 1008 12
4900.2.ck $$\chi_{4900}(451, \cdot)$$ n/a 6312 12
4900.2.co $$\chi_{4900}(67, \cdot)$$ n/a 9472 16
4900.2.cq $$\chi_{4900}(117, \cdot)$$ n/a 1600 16
4900.2.cr $$\chi_{4900}(139, \cdot)$$ n/a 20064 24
4900.2.ct $$\chi_{4900}(29, \cdot)$$ n/a 3360 24
4900.2.cv $$\chi_{4900}(111, \cdot)$$ n/a 20064 24
4900.2.cy $$\chi_{4900}(107, \cdot)$$ n/a 12000 24
4900.2.da $$\chi_{4900}(157, \cdot)$$ n/a 2016 24
4900.2.dc $$\chi_{4900}(81, \cdot)$$ n/a 6720 48
4900.2.dd $$\chi_{4900}(127, \cdot)$$ n/a 40128 48
4900.2.df $$\chi_{4900}(13, \cdot)$$ n/a 6720 48
4900.2.dj $$\chi_{4900}(131, \cdot)$$ n/a 40128 48
4900.2.dl $$\chi_{4900}(9, \cdot)$$ n/a 6720 48
4900.2.dn $$\chi_{4900}(59, \cdot)$$ n/a 40128 48
4900.2.dp $$\chi_{4900}(17, \cdot)$$ n/a 13440 96
4900.2.dr $$\chi_{4900}(23, \cdot)$$ n/a 80256 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4900))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4900)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(700))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(980))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1225))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2450))$$$$^{\oplus 2}$$