## Defining parameters

 Level: $$N$$ = $$4600 = 2^{3} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$2534400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4600))$$.

Total New Old
Modular forms 640992 328960 312032
Cusp forms 626209 325516 300693
Eisenstein series 14783 3444 11339

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4600))$$

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
4600.2.a $$\chi_{4600}(1, \cdot)$$ 4600.2.a.a 1 1
4600.2.a.b 1
4600.2.a.c 1
4600.2.a.d 1
4600.2.a.e 1
4600.2.a.f 1
4600.2.a.g 1
4600.2.a.h 1
4600.2.a.i 1
4600.2.a.j 1
4600.2.a.k 1
4600.2.a.l 1
4600.2.a.m 1
4600.2.a.n 1
4600.2.a.o 1
4600.2.a.p 1
4600.2.a.q 2
4600.2.a.r 2
4600.2.a.s 2
4600.2.a.t 2
4600.2.a.u 2
4600.2.a.v 3
4600.2.a.w 3
4600.2.a.x 3
4600.2.a.y 3
4600.2.a.z 3
4600.2.a.ba 4
4600.2.a.bb 4
4600.2.a.bc 5
4600.2.a.bd 5
4600.2.a.be 5
4600.2.a.bf 5
4600.2.a.bg 5
4600.2.a.bh 7
4600.2.a.bi 7
4600.2.a.bj 8
4600.2.a.bk 8
4600.2.b $$\chi_{4600}(2299, \cdot)$$ n/a 428 1
4600.2.e $$\chi_{4600}(4049, \cdot)$$ 4600.2.e.a 2 1
4600.2.e.b 2
4600.2.e.c 2
4600.2.e.d 2
4600.2.e.e 2
4600.2.e.f 2
4600.2.e.g 2
4600.2.e.h 2
4600.2.e.i 2
4600.2.e.j 2
4600.2.e.k 2
4600.2.e.l 4
4600.2.e.m 4
4600.2.e.n 4
4600.2.e.o 4
4600.2.e.p 6
4600.2.e.q 6
4600.2.e.r 6
4600.2.e.s 6
4600.2.e.t 8
4600.2.e.u 10
4600.2.e.v 10
4600.2.e.w 10
4600.2.f $$\chi_{4600}(2301, \cdot)$$ n/a 418 1
4600.2.i $$\chi_{4600}(551, \cdot)$$ None 0 1
4600.2.j $$\chi_{4600}(1749, \cdot)$$ n/a 396 1
4600.2.m $$\chi_{4600}(4599, \cdot)$$ None 0 1
4600.2.n $$\chi_{4600}(2851, \cdot)$$ n/a 450 1
4600.2.q $$\chi_{4600}(1057, \cdot)$$ n/a 216 2
4600.2.s $$\chi_{4600}(2807, \cdot)$$ None 0 2
4600.2.v $$\chi_{4600}(507, \cdot)$$ n/a 792 2
4600.2.x $$\chi_{4600}(3357, \cdot)$$ n/a 856 2
4600.2.y $$\chi_{4600}(921, \cdot)$$ n/a 664 4
4600.2.z $$\chi_{4600}(919, \cdot)$$ None 0 4
4600.2.bc $$\chi_{4600}(829, \cdot)$$ n/a 2640 4
4600.2.bf $$\chi_{4600}(91, \cdot)$$ n/a 2864 4
4600.2.bg $$\chi_{4600}(369, \cdot)$$ n/a 656 4
4600.2.bj $$\chi_{4600}(459, \cdot)$$ n/a 2864 4
4600.2.bk $$\chi_{4600}(1471, \cdot)$$ None 0 4
4600.2.bn $$\chi_{4600}(461, \cdot)$$ n/a 2640 4
4600.2.bo $$\chi_{4600}(601, \cdot)$$ n/a 1140 10
4600.2.bp $$\chi_{4600}(413, \cdot)$$ n/a 5728 8
4600.2.br $$\chi_{4600}(323, \cdot)$$ n/a 5280 8
4600.2.bu $$\chi_{4600}(47, \cdot)$$ None 0 8
4600.2.bw $$\chi_{4600}(137, \cdot)$$ n/a 1440 8
4600.2.bz $$\chi_{4600}(51, \cdot)$$ n/a 4500 10
4600.2.ca $$\chi_{4600}(199, \cdot)$$ None 0 10
4600.2.cd $$\chi_{4600}(349, \cdot)$$ n/a 4280 10
4600.2.ce $$\chi_{4600}(751, \cdot)$$ None 0 10
4600.2.ch $$\chi_{4600}(101, \cdot)$$ n/a 4500 10
4600.2.ci $$\chi_{4600}(49, \cdot)$$ n/a 1080 10
4600.2.cl $$\chi_{4600}(99, \cdot)$$ n/a 4280 10
4600.2.cm $$\chi_{4600}(157, \cdot)$$ n/a 8560 20
4600.2.co $$\chi_{4600}(243, \cdot)$$ n/a 8560 20
4600.2.cr $$\chi_{4600}(407, \cdot)$$ None 0 20
4600.2.ct $$\chi_{4600}(57, \cdot)$$ n/a 2160 20
4600.2.cu $$\chi_{4600}(41, \cdot)$$ n/a 7200 40
4600.2.cv $$\chi_{4600}(141, \cdot)$$ n/a 28640 40
4600.2.cy $$\chi_{4600}(111, \cdot)$$ None 0 40
4600.2.cz $$\chi_{4600}(19, \cdot)$$ n/a 28640 40
4600.2.dc $$\chi_{4600}(9, \cdot)$$ n/a 7200 40
4600.2.dd $$\chi_{4600}(11, \cdot)$$ n/a 28640 40
4600.2.dg $$\chi_{4600}(29, \cdot)$$ n/a 28640 40
4600.2.dj $$\chi_{4600}(79, \cdot)$$ None 0 40
4600.2.dk $$\chi_{4600}(17, \cdot)$$ n/a 14400 80
4600.2.dm $$\chi_{4600}(87, \cdot)$$ None 0 80
4600.2.dp $$\chi_{4600}(3, \cdot)$$ n/a 57280 80
4600.2.dr $$\chi_{4600}(37, \cdot)$$ n/a 57280 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4600))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4600)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(920))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1150))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2300))$$$$^{\oplus 2}$$