## Defining parameters

 Level: $$N$$ = $$4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$2709504$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4998))$$.

Total New Old
Modular forms 685056 161378 523678
Cusp forms 669697 161378 508319
Eisenstein series 15359 0 15359

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4998))$$

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
4998.2.a $$\chi_{4998}(1, \cdot)$$ 4998.2.a.a 1 1
4998.2.a.b 1
4998.2.a.c 1
4998.2.a.d 1
4998.2.a.e 1
4998.2.a.f 1
4998.2.a.g 1
4998.2.a.h 1
4998.2.a.i 1
4998.2.a.j 1
4998.2.a.k 1
4998.2.a.l 1
4998.2.a.m 1
4998.2.a.n 1
4998.2.a.o 1
4998.2.a.p 1
4998.2.a.q 1
4998.2.a.r 1
4998.2.a.s 1
4998.2.a.t 1
4998.2.a.u 1
4998.2.a.v 1
4998.2.a.w 1
4998.2.a.x 1
4998.2.a.y 1
4998.2.a.z 1
4998.2.a.ba 1
4998.2.a.bb 1
4998.2.a.bc 1
4998.2.a.bd 1
4998.2.a.be 1
4998.2.a.bf 1
4998.2.a.bg 1
4998.2.a.bh 1
4998.2.a.bi 1
4998.2.a.bj 1
4998.2.a.bk 1
4998.2.a.bl 1
4998.2.a.bm 1
4998.2.a.bn 1
4998.2.a.bo 1
4998.2.a.bp 1
4998.2.a.bq 1
4998.2.a.br 1
4998.2.a.bs 2
4998.2.a.bt 2
4998.2.a.bu 2
4998.2.a.bv 2
4998.2.a.bw 2
4998.2.a.bx 2
4998.2.a.by 2
4998.2.a.bz 2
4998.2.a.ca 2
4998.2.a.cb 2
4998.2.a.cc 2
4998.2.a.cd 2
4998.2.a.ce 2
4998.2.a.cf 2
4998.2.a.cg 3
4998.2.a.ch 3
4998.2.a.ci 3
4998.2.a.cj 3
4998.2.a.ck 4
4998.2.a.cl 4
4998.2.a.cm 4
4998.2.a.cn 4
4998.2.a.co 4
4998.2.a.cp 4
4998.2.b $$\chi_{4998}(883, \cdot)$$ n/a 122 1
4998.2.e $$\chi_{4998}(4997, \cdot)$$ n/a 240 1
4998.2.f $$\chi_{4998}(4115, \cdot)$$ n/a 216 1
4998.2.i $$\chi_{4998}(4183, \cdot)$$ n/a 216 2
4998.2.k $$\chi_{4998}(293, \cdot)$$ n/a 480 2
4998.2.m $$\chi_{4998}(1177, \cdot)$$ n/a 244 2
4998.2.p $$\chi_{4998}(4625, \cdot)$$ n/a 424 2
4998.2.q $$\chi_{4998}(509, \cdot)$$ n/a 480 2
4998.2.t $$\chi_{4998}(67, \cdot)$$ n/a 240 2
4998.2.u $$\chi_{4998}(715, \cdot)$$ n/a 912 6
4998.2.v $$\chi_{4998}(1471, \cdot)$$ n/a 496 4
4998.2.x $$\chi_{4998}(587, \cdot)$$ n/a 960 4
4998.2.z $$\chi_{4998}(803, \cdot)$$ n/a 960 4
4998.2.bb $$\chi_{4998}(361, \cdot)$$ n/a 480 4
4998.2.be $$\chi_{4998}(545, \cdot)$$ n/a 1776 6
4998.2.bh $$\chi_{4998}(713, \cdot)$$ n/a 2016 6
4998.2.bi $$\chi_{4998}(169, \cdot)$$ n/a 1008 6
4998.2.bm $$\chi_{4998}(97, \cdot)$$ n/a 960 8
4998.2.bn $$\chi_{4998}(197, \cdot)$$ n/a 1968 8
4998.2.bo $$\chi_{4998}(205, \cdot)$$ n/a 1776 12
4998.2.bq $$\chi_{4998}(655, \cdot)$$ n/a 960 8
4998.2.bs $$\chi_{4998}(1097, \cdot)$$ n/a 1920 8
4998.2.bt $$\chi_{4998}(421, \cdot)$$ n/a 2016 12
4998.2.bv $$\chi_{4998}(251, \cdot)$$ n/a 4032 12
4998.2.by $$\chi_{4998}(781, \cdot)$$ n/a 2016 12
4998.2.bz $$\chi_{4998}(101, \cdot)$$ n/a 4032 12
4998.2.cc $$\chi_{4998}(341, \cdot)$$ n/a 3600 12
4998.2.ce $$\chi_{4998}(275, \cdot)$$ n/a 3840 16
4998.2.cf $$\chi_{4998}(31, \cdot)$$ n/a 1920 16
4998.2.cj $$\chi_{4998}(83, \cdot)$$ n/a 8064 24
4998.2.cl $$\chi_{4998}(43, \cdot)$$ n/a 4032 24
4998.2.cn $$\chi_{4998}(319, \cdot)$$ n/a 4032 24
4998.2.cp $$\chi_{4998}(47, \cdot)$$ n/a 8064 24
4998.2.cq $$\chi_{4998}(29, \cdot)$$ n/a 16128 48
4998.2.cr $$\chi_{4998}(139, \cdot)$$ n/a 8064 48
4998.2.cu $$\chi_{4998}(59, \cdot)$$ n/a 16128 48
4998.2.cw $$\chi_{4998}(25, \cdot)$$ n/a 8064 48
4998.2.da $$\chi_{4998}(61, \cdot)$$ n/a 16128 96
4998.2.db $$\chi_{4998}(11, \cdot)$$ n/a 32256 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4998))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4998)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(357))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(714))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(833))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1666))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2499))$$$$^{\oplus 2}$$