# Properties

 Label 5635.2 Level 5635 Weight 2 Dimension 1082136 Nonzero newspaces 48 Sturm bound 4967424

## Defining parameters

 Level: $$N$$ = $$5635 = 5 \cdot 7^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$4967424$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5635))$$.

Total New Old
Modular forms 1252416 1094360 158056
Cusp forms 1231297 1082136 149161
Eisenstein series 21119 12224 8895

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5635))$$

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
5635.2.a $$\chi_{5635}(1, \cdot)$$ 5635.2.a.a 1 1
5635.2.a.b 1
5635.2.a.c 1
5635.2.a.d 1
5635.2.a.e 1
5635.2.a.f 1
5635.2.a.g 1
5635.2.a.h 1
5635.2.a.i 1
5635.2.a.j 1
5635.2.a.k 1
5635.2.a.l 1
5635.2.a.m 1
5635.2.a.n 2
5635.2.a.o 2
5635.2.a.p 2
5635.2.a.q 2
5635.2.a.r 3
5635.2.a.s 4
5635.2.a.t 4
5635.2.a.u 4
5635.2.a.v 4
5635.2.a.w 4
5635.2.a.x 5
5635.2.a.y 5
5635.2.a.z 6
5635.2.a.ba 6
5635.2.a.bb 8
5635.2.a.bc 12
5635.2.a.bd 12
5635.2.a.be 13
5635.2.a.bf 13
5635.2.a.bg 13
5635.2.a.bh 13
5635.2.a.bi 15
5635.2.a.bj 15
5635.2.a.bk 16
5635.2.a.bl 16
5635.2.a.bm 17
5635.2.a.bn 17
5635.2.a.bo 28
5635.2.a.bp 28
5635.2.c $$\chi_{5635}(4509, \cdot)$$ n/a 450 1
5635.2.d $$\chi_{5635}(5634, \cdot)$$ n/a 472 1
5635.2.f $$\chi_{5635}(1126, \cdot)$$ n/a 320 1
5635.2.i $$\chi_{5635}(116, \cdot)$$ n/a 584 2
5635.2.k $$\chi_{5635}(783, \cdot)$$ n/a 880 2
5635.2.l $$\chi_{5635}(2598, \cdot)$$ n/a 964 2
5635.2.p $$\chi_{5635}(1011, \cdot)$$ n/a 640 2
5635.2.r $$\chi_{5635}(3449, \cdot)$$ n/a 944 2
5635.2.s $$\chi_{5635}(1059, \cdot)$$ n/a 880 2
5635.2.u $$\chi_{5635}(806, \cdot)$$ n/a 2448 6
5635.2.v $$\chi_{5635}(246, \cdot)$$ n/a 3280 10
5635.2.w $$\chi_{5635}(668, \cdot)$$ n/a 1760 4
5635.2.z $$\chi_{5635}(1402, \cdot)$$ n/a 1888 4
5635.2.bc $$\chi_{5635}(321, \cdot)$$ n/a 2688 6
5635.2.be $$\chi_{5635}(804, \cdot)$$ n/a 4008 6
5635.2.bf $$\chi_{5635}(484, \cdot)$$ n/a 3696 6
5635.2.bh $$\chi_{5635}(576, \cdot)$$ n/a 4944 12
5635.2.bk $$\chi_{5635}(636, \cdot)$$ n/a 3200 10
5635.2.bm $$\chi_{5635}(244, \cdot)$$ n/a 4720 10
5635.2.bn $$\chi_{5635}(834, \cdot)$$ n/a 4820 10
5635.2.bq $$\chi_{5635}(22, \cdot)$$ n/a 8016 12
5635.2.br $$\chi_{5635}(622, \cdot)$$ n/a 7392 12
5635.2.bt $$\chi_{5635}(361, \cdot)$$ n/a 6400 20
5635.2.bv $$\chi_{5635}(254, \cdot)$$ n/a 7392 12
5635.2.bw $$\chi_{5635}(229, \cdot)$$ n/a 8016 12
5635.2.by $$\chi_{5635}(206, \cdot)$$ n/a 5376 12
5635.2.cc $$\chi_{5635}(148, \cdot)$$ n/a 9640 20
5635.2.cd $$\chi_{5635}(48, \cdot)$$ n/a 9440 20
5635.2.cg $$\chi_{5635}(324, \cdot)$$ n/a 9440 20
5635.2.ch $$\chi_{5635}(19, \cdot)$$ n/a 9440 20
5635.2.cj $$\chi_{5635}(166, \cdot)$$ n/a 6400 20
5635.2.cm $$\chi_{5635}(36, \cdot)$$ n/a 26880 60
5635.2.cn $$\chi_{5635}(137, \cdot)$$ n/a 16032 24
5635.2.cq $$\chi_{5635}(47, \cdot)$$ n/a 14784 24
5635.2.cr $$\chi_{5635}(67, \cdot)$$ n/a 18880 40
5635.2.cu $$\chi_{5635}(117, \cdot)$$ n/a 18880 40
5635.2.cw $$\chi_{5635}(29, \cdot)$$ n/a 40080 60
5635.2.cx $$\chi_{5635}(34, \cdot)$$ n/a 40080 60
5635.2.cz $$\chi_{5635}(76, \cdot)$$ n/a 26880 60
5635.2.dc $$\chi_{5635}(16, \cdot)$$ n/a 53760 120
5635.2.de $$\chi_{5635}(13, \cdot)$$ n/a 80160 120
5635.2.df $$\chi_{5635}(43, \cdot)$$ n/a 80160 120
5635.2.dj $$\chi_{5635}(61, \cdot)$$ n/a 53760 120
5635.2.dl $$\chi_{5635}(89, \cdot)$$ n/a 80160 120
5635.2.dm $$\chi_{5635}(4, \cdot)$$ n/a 80160 120
5635.2.do $$\chi_{5635}(3, \cdot)$$ n/a 160320 240
5635.2.dr $$\chi_{5635}(37, \cdot)$$ n/a 160320 240

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5635))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5635)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(805))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1127))$$$$^{\oplus 2}$$