# Properties

 Label 8712.2 Level 8712 Weight 2 Dimension 913240 Nonzero newspaces 48 Sturm bound 8363520

## Defining parameters

 Level: $$N$$ = $$8712 = 2^{3} \cdot 3^{2} \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$8363520$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8712))$$.

Total New Old
Modular forms 2106240 918298 1187942
Cusp forms 2075521 913240 1162281
Eisenstein series 30719 5058 25661

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8712))$$

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
8712.2.a $$\chi_{8712}(1, \cdot)$$ 8712.2.a.a 1 1
8712.2.a.b 1
8712.2.a.c 1
8712.2.a.d 1
8712.2.a.e 1
8712.2.a.f 1
8712.2.a.g 1
8712.2.a.h 1
8712.2.a.i 1
8712.2.a.j 1
8712.2.a.k 1
8712.2.a.l 1
8712.2.a.m 1
8712.2.a.n 1
8712.2.a.o 1
8712.2.a.p 1
8712.2.a.q 1
8712.2.a.r 1
8712.2.a.s 1
8712.2.a.t 1
8712.2.a.u 1
8712.2.a.v 1
8712.2.a.w 1
8712.2.a.x 1
8712.2.a.y 1
8712.2.a.z 1
8712.2.a.ba 2
8712.2.a.bb 2
8712.2.a.bc 2
8712.2.a.bd 2
8712.2.a.be 2
8712.2.a.bf 2
8712.2.a.bg 2
8712.2.a.bh 2
8712.2.a.bi 2
8712.2.a.bj 2
8712.2.a.bk 2
8712.2.a.bl 2
8712.2.a.bm 2
8712.2.a.bn 2
8712.2.a.bo 2
8712.2.a.bp 2
8712.2.a.bq 2
8712.2.a.br 2
8712.2.a.bs 2
8712.2.a.bt 2
8712.2.a.bu 2
8712.2.a.bv 3
8712.2.a.bw 3
8712.2.a.bx 3
8712.2.a.by 3
8712.2.a.bz 4
8712.2.a.ca 4
8712.2.a.cb 4
8712.2.a.cc 4
8712.2.a.cd 4
8712.2.a.ce 4
8712.2.a.cf 4
8712.2.a.cg 4
8712.2.a.ch 6
8712.2.a.ci 6
8712.2.a.cj 6
8712.2.a.ck 6
8712.2.b $$\chi_{8712}(2177, \cdot)$$ n/a 108 1
8712.2.d $$\chi_{8712}(2663, \cdot)$$ None 0 1
8712.2.f $$\chi_{8712}(4357, \cdot)$$ n/a 536 1
8712.2.h $$\chi_{8712}(8227, \cdot)$$ n/a 532 1
8712.2.k $$\chi_{8712}(7019, \cdot)$$ n/a 436 1
8712.2.m $$\chi_{8712}(6533, \cdot)$$ n/a 432 1
8712.2.o $$\chi_{8712}(3871, \cdot)$$ None 0 1
8712.2.q $$\chi_{8712}(2905, \cdot)$$ n/a 654 2
8712.2.r $$\chi_{8712}(1945, \cdot)$$ n/a 540 4
8712.2.u $$\chi_{8712}(967, \cdot)$$ None 0 2
8712.2.w $$\chi_{8712}(725, \cdot)$$ n/a 2560 2
8712.2.y $$\chi_{8712}(1211, \cdot)$$ n/a 2580 2
8712.2.z $$\chi_{8712}(2419, \cdot)$$ n/a 2560 2
8712.2.bb $$\chi_{8712}(1453, \cdot)$$ n/a 2580 2
8712.2.bd $$\chi_{8712}(5567, \cdot)$$ None 0 2
8712.2.bf $$\chi_{8712}(5081, \cdot)$$ n/a 648 2
8712.2.bi $$\chi_{8712}(1207, \cdot)$$ None 0 4
8712.2.bk $$\chi_{8712}(3869, \cdot)$$ n/a 1728 4
8712.2.bm $$\chi_{8712}(251, \cdot)$$ n/a 1728 4
8712.2.bp $$\chi_{8712}(5563, \cdot)$$ n/a 2128 4
8712.2.br $$\chi_{8712}(4141, \cdot)$$ n/a 2128 4
8712.2.bt $$\chi_{8712}(2447, \cdot)$$ None 0 4
8712.2.bv $$\chi_{8712}(161, \cdot)$$ n/a 432 4
8712.2.bw $$\chi_{8712}(793, \cdot)$$ n/a 1650 10
8712.2.bx $$\chi_{8712}(2689, \cdot)$$ n/a 2592 8
8712.2.bz $$\chi_{8712}(703, \cdot)$$ None 0 10
8712.2.cb $$\chi_{8712}(197, \cdot)$$ n/a 5280 10
8712.2.cd $$\chi_{8712}(683, \cdot)$$ n/a 5280 10
8712.2.cg $$\chi_{8712}(307, \cdot)$$ n/a 6580 10
8712.2.ci $$\chi_{8712}(397, \cdot)$$ n/a 6580 10
8712.2.ck $$\chi_{8712}(287, \cdot)$$ None 0 10
8712.2.cm $$\chi_{8712}(593, \cdot)$$ n/a 1320 10
8712.2.co $$\chi_{8712}(2417, \cdot)$$ n/a 2592 8
8712.2.cq $$\chi_{8712}(1703, \cdot)$$ None 0 8
8712.2.cs $$\chi_{8712}(493, \cdot)$$ n/a 10240 8
8712.2.cu $$\chi_{8712}(403, \cdot)$$ n/a 10240 8
8712.2.cv $$\chi_{8712}(995, \cdot)$$ n/a 10240 8
8712.2.cx $$\chi_{8712}(941, \cdot)$$ n/a 10240 8
8712.2.cz $$\chi_{8712}(1183, \cdot)$$ None 0 8
8712.2.dc $$\chi_{8712}(265, \cdot)$$ n/a 7920 20
8712.2.dd $$\chi_{8712}(289, \cdot)$$ n/a 6600 40
8712.2.df $$\chi_{8712}(65, \cdot)$$ n/a 7920 20
8712.2.dh $$\chi_{8712}(23, \cdot)$$ None 0 20
8712.2.dj $$\chi_{8712}(133, \cdot)$$ n/a 31600 20
8712.2.dl $$\chi_{8712}(43, \cdot)$$ n/a 31600 20
8712.2.dm $$\chi_{8712}(155, \cdot)$$ n/a 31600 20
8712.2.do $$\chi_{8712}(461, \cdot)$$ n/a 31600 20
8712.2.dq $$\chi_{8712}(175, \cdot)$$ None 0 20
8712.2.dt $$\chi_{8712}(17, \cdot)$$ n/a 5280 40
8712.2.dv $$\chi_{8712}(71, \cdot)$$ None 0 40
8712.2.dx $$\chi_{8712}(37, \cdot)$$ n/a 26320 40
8712.2.dz $$\chi_{8712}(19, \cdot)$$ n/a 26320 40
8712.2.ec $$\chi_{8712}(179, \cdot)$$ n/a 21120 40
8712.2.ee $$\chi_{8712}(413, \cdot)$$ n/a 21120 40
8712.2.eg $$\chi_{8712}(127, \cdot)$$ None 0 40
8712.2.ei $$\chi_{8712}(25, \cdot)$$ n/a 31680 80
8712.2.el $$\chi_{8712}(7, \cdot)$$ None 0 80
8712.2.en $$\chi_{8712}(29, \cdot)$$ n/a 126400 80
8712.2.ep $$\chi_{8712}(59, \cdot)$$ n/a 126400 80
8712.2.eq $$\chi_{8712}(139, \cdot)$$ n/a 126400 80
8712.2.es $$\chi_{8712}(157, \cdot)$$ n/a 126400 80
8712.2.eu $$\chi_{8712}(47, \cdot)$$ None 0 80
8712.2.ew $$\chi_{8712}(41, \cdot)$$ n/a 31680 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8712))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8712)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(484))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(726))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(792))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(968))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1089))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1452))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2178))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2904))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4356))$$$$^{\oplus 2}$$