# Properties

 Label 4719.2 Level 4719 Weight 2 Dimension 589568 Nonzero newspaces 48 Sturm bound 3252480

## Defining parameters

 Level: $$N$$ = $$4719 = 3 \cdot 11^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$3252480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4719))$$.

Total New Old
Modular forms 820800 595752 225048
Cusp forms 805441 589568 215873
Eisenstein series 15359 6184 9175

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4719))$$

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
4719.2.a $$\chi_{4719}(1, \cdot)$$ 4719.2.a.a 1 1
4719.2.a.b 1
4719.2.a.c 1
4719.2.a.d 1
4719.2.a.e 1
4719.2.a.f 1
4719.2.a.g 1
4719.2.a.h 1
4719.2.a.i 1
4719.2.a.j 1
4719.2.a.k 1
4719.2.a.l 1
4719.2.a.m 1
4719.2.a.n 2
4719.2.a.o 2
4719.2.a.p 2
4719.2.a.q 3
4719.2.a.r 3
4719.2.a.s 3
4719.2.a.t 3
4719.2.a.u 3
4719.2.a.v 3
4719.2.a.w 3
4719.2.a.x 4
4719.2.a.y 4
4719.2.a.z 4
4719.2.a.ba 5
4719.2.a.bb 5
4719.2.a.bc 5
4719.2.a.bd 5
4719.2.a.be 5
4719.2.a.bf 5
4719.2.a.bg 6
4719.2.a.bh 6
4719.2.a.bi 10
4719.2.a.bj 10
4719.2.a.bk 10
4719.2.a.bl 10
4719.2.a.bm 10
4719.2.a.bn 10
4719.2.a.bo 14
4719.2.a.bp 14
4719.2.a.bq 18
4719.2.a.br 18
4719.2.b $$\chi_{4719}(727, \cdot)$$ n/a 254 1
4719.2.e $$\chi_{4719}(4718, \cdot)$$ n/a 488 1
4719.2.f $$\chi_{4719}(3992, \cdot)$$ n/a 432 1
4719.2.i $$\chi_{4719}(1816, \cdot)$$ n/a 510 2
4719.2.j $$\chi_{4719}(122, \cdot)$$ n/a 980 2
4719.2.m $$\chi_{4719}(967, \cdot)$$ n/a 504 2
4719.2.n $$\chi_{4719}(1600, \cdot)$$ n/a 864 4
4719.2.p $$\chi_{4719}(1088, \cdot)$$ n/a 976 2
4719.2.s $$\chi_{4719}(1453, \cdot)$$ n/a 506 2
4719.2.t $$\chi_{4719}(725, \cdot)$$ n/a 976 2
4719.2.x $$\chi_{4719}(1613, \cdot)$$ n/a 1728 4
4719.2.y $$\chi_{4719}(233, \cdot)$$ n/a 1952 4
4719.2.bb $$\chi_{4719}(493, \cdot)$$ n/a 1008 4
4719.2.bc $$\chi_{4719}(430, \cdot)$$ n/a 2640 10
4719.2.be $$\chi_{4719}(241, \cdot)$$ n/a 1008 4
4719.2.bf $$\chi_{4719}(1211, \cdot)$$ n/a 1964 4
4719.2.bh $$\chi_{4719}(874, \cdot)$$ n/a 2016 8
4719.2.bj $$\chi_{4719}(632, \cdot)$$ n/a 3904 8
4719.2.bk $$\chi_{4719}(112, \cdot)$$ n/a 2016 8
4719.2.bo $$\chi_{4719}(131, \cdot)$$ n/a 5280 10
4719.2.bp $$\chi_{4719}(428, \cdot)$$ n/a 6120 10
4719.2.bs $$\chi_{4719}(298, \cdot)$$ n/a 3080 10
4719.2.bu $$\chi_{4719}(524, \cdot)$$ n/a 3904 8
4719.2.bv $$\chi_{4719}(511, \cdot)$$ n/a 2016 8
4719.2.by $$\chi_{4719}(887, \cdot)$$ n/a 3904 8
4719.2.ca $$\chi_{4719}(100, \cdot)$$ n/a 6160 20
4719.2.cb $$\chi_{4719}(109, \cdot)$$ n/a 6160 20
4719.2.ce $$\chi_{4719}(320, \cdot)$$ n/a 12240 20
4719.2.cf $$\chi_{4719}(157, \cdot)$$ n/a 10560 40
4719.2.cg $$\chi_{4719}(457, \cdot)$$ n/a 4032 16
4719.2.cj $$\chi_{4719}(245, \cdot)$$ n/a 7808 16
4719.2.cl $$\chi_{4719}(296, \cdot)$$ n/a 12240 20
4719.2.cm $$\chi_{4719}(166, \cdot)$$ n/a 6160 20
4719.2.cp $$\chi_{4719}(230, \cdot)$$ n/a 12240 20
4719.2.cr $$\chi_{4719}(25, \cdot)$$ n/a 12320 40
4719.2.cu $$\chi_{4719}(116, \cdot)$$ n/a 24480 40
4719.2.cv $$\chi_{4719}(248, \cdot)$$ n/a 21120 40
4719.2.cz $$\chi_{4719}(89, \cdot)$$ n/a 24480 40
4719.2.da $$\chi_{4719}(76, \cdot)$$ n/a 12320 40
4719.2.dc $$\chi_{4719}(16, \cdot)$$ n/a 24640 80
4719.2.de $$\chi_{4719}(73, \cdot)$$ n/a 24640 80
4719.2.df $$\chi_{4719}(5, \cdot)$$ n/a 48960 80
4719.2.di $$\chi_{4719}(29, \cdot)$$ n/a 48960 80
4719.2.dl $$\chi_{4719}(4, \cdot)$$ n/a 24640 80
4719.2.dm $$\chi_{4719}(17, \cdot)$$ n/a 48960 80
4719.2.do $$\chi_{4719}(20, \cdot)$$ n/a 97920 160
4719.2.dr $$\chi_{4719}(7, \cdot)$$ n/a 49280 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4719))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4719)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(429))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1573))$$$$^{\oplus 2}$$