## Defining parameters

 Level: $$N$$ = $$4840 = 2^{3} \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$2787840$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4840))$$.

Total New Old
Modular forms 704640 355141 349499
Cusp forms 689281 351769 337512
Eisenstein series 15359 3372 11987

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4840))$$

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
4840.2.a $$\chi_{4840}(1, \cdot)$$ 4840.2.a.a 1 1
4840.2.a.b 1
4840.2.a.c 1
4840.2.a.d 1
4840.2.a.e 1
4840.2.a.f 1
4840.2.a.g 1
4840.2.a.h 1
4840.2.a.i 1
4840.2.a.j 2
4840.2.a.k 2
4840.2.a.l 2
4840.2.a.m 2
4840.2.a.n 2
4840.2.a.o 2
4840.2.a.p 2
4840.2.a.q 3
4840.2.a.r 3
4840.2.a.s 3
4840.2.a.t 3
4840.2.a.u 3
4840.2.a.v 3
4840.2.a.w 4
4840.2.a.x 4
4840.2.a.y 4
4840.2.a.z 4
4840.2.a.ba 6
4840.2.a.bb 6
4840.2.a.bc 6
4840.2.a.bd 6
4840.2.a.be 6
4840.2.a.bf 6
4840.2.a.bg 8
4840.2.a.bh 8
4840.2.b $$\chi_{4840}(969, \cdot)$$ n/a 164 1
4840.2.c $$\chi_{4840}(2419, \cdot)$$ n/a 632 1
4840.2.f $$\chi_{4840}(3871, \cdot)$$ None 0 1
4840.2.g $$\chi_{4840}(2421, \cdot)$$ n/a 436 1
4840.2.l $$\chi_{4840}(3389, \cdot)$$ n/a 636 1
4840.2.m $$\chi_{4840}(4839, \cdot)$$ None 0 1
4840.2.p $$\chi_{4840}(1451, \cdot)$$ n/a 432 1
4840.2.r $$\chi_{4840}(243, \cdot)$$ n/a 1272 2
4840.2.t $$\chi_{4840}(1693, \cdot)$$ n/a 1264 2
4840.2.v $$\chi_{4840}(2177, \cdot)$$ n/a 324 2
4840.2.x $$\chi_{4840}(727, \cdot)$$ None 0 2
4840.2.y $$\chi_{4840}(81, \cdot)$$ n/a 432 4
4840.2.z $$\chi_{4840}(1371, \cdot)$$ n/a 1728 4
4840.2.bc $$\chi_{4840}(239, \cdot)$$ None 0 4
4840.2.bd $$\chi_{4840}(269, \cdot)$$ n/a 2528 4
4840.2.bi $$\chi_{4840}(1461, \cdot)$$ n/a 1728 4
4840.2.bj $$\chi_{4840}(2151, \cdot)$$ None 0 4
4840.2.bm $$\chi_{4840}(699, \cdot)$$ n/a 2528 4
4840.2.bn $$\chi_{4840}(9, \cdot)$$ n/a 648 4
4840.2.bo $$\chi_{4840}(441, \cdot)$$ n/a 1320 10
4840.2.bp $$\chi_{4840}(233, \cdot)$$ n/a 1296 8
4840.2.br $$\chi_{4840}(487, \cdot)$$ None 0 8
4840.2.bt $$\chi_{4840}(3, \cdot)$$ n/a 5056 8
4840.2.bv $$\chi_{4840}(717, \cdot)$$ n/a 5056 8
4840.2.bz $$\chi_{4840}(221, \cdot)$$ n/a 5280 10
4840.2.ca $$\chi_{4840}(351, \cdot)$$ None 0 10
4840.2.cd $$\chi_{4840}(219, \cdot)$$ n/a 7880 10
4840.2.ce $$\chi_{4840}(89, \cdot)$$ n/a 1980 10
4840.2.cf $$\chi_{4840}(131, \cdot)$$ n/a 5280 10
4840.2.ci $$\chi_{4840}(439, \cdot)$$ None 0 10
4840.2.cj $$\chi_{4840}(309, \cdot)$$ n/a 7880 10
4840.2.cm $$\chi_{4840}(23, \cdot)$$ None 0 20
4840.2.co $$\chi_{4840}(153, \cdot)$$ n/a 3960 20
4840.2.cq $$\chi_{4840}(197, \cdot)$$ n/a 15760 20
4840.2.cs $$\chi_{4840}(67, \cdot)$$ n/a 15760 20
4840.2.cu $$\chi_{4840}(201, \cdot)$$ n/a 5280 40
4840.2.cx $$\chi_{4840}(69, \cdot)$$ n/a 31520 40
4840.2.cy $$\chi_{4840}(39, \cdot)$$ None 0 40
4840.2.db $$\chi_{4840}(51, \cdot)$$ n/a 21120 40
4840.2.dc $$\chi_{4840}(49, \cdot)$$ n/a 7920 40
4840.2.dd $$\chi_{4840}(19, \cdot)$$ n/a 31520 40
4840.2.dg $$\chi_{4840}(151, \cdot)$$ None 0 40
4840.2.dh $$\chi_{4840}(141, \cdot)$$ n/a 21120 40
4840.2.dl $$\chi_{4840}(13, \cdot)$$ n/a 63040 80
4840.2.dn $$\chi_{4840}(147, \cdot)$$ n/a 63040 80
4840.2.dp $$\chi_{4840}(47, \cdot)$$ None 0 80
4840.2.dr $$\chi_{4840}(17, \cdot)$$ n/a 15840 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4840))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4840)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(484))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(605))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(968))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1210))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2420))$$$$^{\oplus 2}$$