# Properties

 Label 7056.2 Level 7056 Weight 2 Dimension 576956 Nonzero newspaces 80 Sturm bound 5419008

## Defining parameters

 Level: $$N$$ = $$7056 = 2^{4} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$5419008$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7056))$$.

Total New Old
Modular forms 1368192 580885 787307
Cusp forms 1341313 576956 764357
Eisenstein series 26879 3929 22950

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7056))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
7056.2.a $$\chi_{7056}(1, \cdot)$$ 7056.2.a.a 1 1
7056.2.a.b 1
7056.2.a.c 1
7056.2.a.d 1
7056.2.a.e 1
7056.2.a.f 1
7056.2.a.g 1
7056.2.a.h 1
7056.2.a.i 1
7056.2.a.j 1
7056.2.a.k 1
7056.2.a.l 1
7056.2.a.m 1
7056.2.a.n 1
7056.2.a.o 1
7056.2.a.p 1
7056.2.a.q 1
7056.2.a.r 1
7056.2.a.s 1
7056.2.a.t 1
7056.2.a.u 1
7056.2.a.v 1
7056.2.a.w 1
7056.2.a.x 1
7056.2.a.y 1
7056.2.a.z 1
7056.2.a.ba 1
7056.2.a.bb 1
7056.2.a.bc 1
7056.2.a.bd 1
7056.2.a.be 1
7056.2.a.bf 1
7056.2.a.bg 1
7056.2.a.bh 1
7056.2.a.bi 1
7056.2.a.bj 1
7056.2.a.bk 1
7056.2.a.bl 1
7056.2.a.bm 1
7056.2.a.bn 1
7056.2.a.bo 1
7056.2.a.bp 1
7056.2.a.bq 1
7056.2.a.br 1
7056.2.a.bs 1
7056.2.a.bt 1
7056.2.a.bu 1
7056.2.a.bv 1
7056.2.a.bw 1
7056.2.a.bx 1
7056.2.a.by 1
7056.2.a.bz 1
7056.2.a.ca 1
7056.2.a.cb 1
7056.2.a.cc 1
7056.2.a.cd 1
7056.2.a.ce 2
7056.2.a.cf 2
7056.2.a.cg 2
7056.2.a.ch 2
7056.2.a.ci 2
7056.2.a.cj 2
7056.2.a.ck 2
7056.2.a.cl 2
7056.2.a.cm 2
7056.2.a.cn 2
7056.2.a.co 2
7056.2.a.cp 2
7056.2.a.cq 2
7056.2.a.cr 2
7056.2.a.cs 2
7056.2.a.ct 2
7056.2.a.cu 2
7056.2.a.cv 2
7056.2.a.cw 2
7056.2.a.cx 2
7056.2.a.cy 4
7056.2.b $$\chi_{7056}(1567, \cdot)$$ 7056.2.b.a 2 1
7056.2.b.b 2
7056.2.b.c 2
7056.2.b.d 2
7056.2.b.e 2
7056.2.b.f 2
7056.2.b.g 2
7056.2.b.h 2
7056.2.b.i 2
7056.2.b.j 2
7056.2.b.k 2
7056.2.b.l 2
7056.2.b.m 2
7056.2.b.n 2
7056.2.b.o 4
7056.2.b.p 4
7056.2.b.q 4
7056.2.b.r 4
7056.2.b.s 4
7056.2.b.t 4
7056.2.b.u 4
7056.2.b.v 4
7056.2.b.w 8
7056.2.b.x 8
7056.2.b.y 8
7056.2.b.z 16
7056.2.c $$\chi_{7056}(3529, \cdot)$$ None 0 1
7056.2.h $$\chi_{7056}(4607, \cdot)$$ 7056.2.h.a 2 1
7056.2.h.b 2
7056.2.h.c 2
7056.2.h.d 4
7056.2.h.e 4
7056.2.h.f 4
7056.2.h.g 4
7056.2.h.h 4
7056.2.h.i 4
7056.2.h.j 4
7056.2.h.k 8
7056.2.h.l 8
7056.2.h.m 8
7056.2.h.n 12
7056.2.h.o 12
7056.2.i $$\chi_{7056}(4409, \cdot)$$ None 0 1
7056.2.j $$\chi_{7056}(1079, \cdot)$$ None 0 1
7056.2.k $$\chi_{7056}(881, \cdot)$$ 7056.2.k.a 4 1
7056.2.k.b 4
7056.2.k.c 8
7056.2.k.d 8
7056.2.k.e 8
7056.2.k.f 8
7056.2.k.g 8
7056.2.k.h 16
7056.2.k.i 16
7056.2.p $$\chi_{7056}(5095, \cdot)$$ None 0 1
7056.2.q $$\chi_{7056}(1537, \cdot)$$ n/a 472 2
7056.2.r $$\chi_{7056}(2353, \cdot)$$ n/a 482 2
7056.2.s $$\chi_{7056}(3313, \cdot)$$ n/a 196 2
7056.2.t $$\chi_{7056}(961, \cdot)$$ n/a 472 2
7056.2.v $$\chi_{7056}(2843, \cdot)$$ n/a 656 2
7056.2.x $$\chi_{7056}(3331, \cdot)$$ n/a 792 2
7056.2.z $$\chi_{7056}(1765, \cdot)$$ n/a 810 2
7056.2.bb $$\chi_{7056}(2645, \cdot)$$ n/a 640 2
7056.2.be $$\chi_{7056}(2713, \cdot)$$ None 0 2
7056.2.bf $$\chi_{7056}(31, \cdot)$$ n/a 480 2
7056.2.bg $$\chi_{7056}(3449, \cdot)$$ None 0 2
7056.2.bh $$\chi_{7056}(3215, \cdot)$$ n/a 480 2
7056.2.bm $$\chi_{7056}(391, \cdot)$$ None 0 2
7056.2.bn $$\chi_{7056}(4135, \cdot)$$ None 0 2
7056.2.bs $$\chi_{7056}(1207, \cdot)$$ None 0 2
7056.2.bt $$\chi_{7056}(4049, \cdot)$$ n/a 160 2
7056.2.bu $$\chi_{7056}(4391, \cdot)$$ None 0 2
7056.2.bz $$\chi_{7056}(3431, \cdot)$$ None 0 2
7056.2.ca $$\chi_{7056}(2273, \cdot)$$ n/a 472 2
7056.2.cb $$\chi_{7056}(263, \cdot)$$ None 0 2
7056.2.cc $$\chi_{7056}(3233, \cdot)$$ n/a 472 2
7056.2.ch $$\chi_{7056}(2255, \cdot)$$ n/a 492 2
7056.2.ci $$\chi_{7056}(2873, \cdot)$$ None 0 2
7056.2.cj $$\chi_{7056}(3791, \cdot)$$ n/a 480 2
7056.2.ck $$\chi_{7056}(2057, \cdot)$$ None 0 2
7056.2.cp $$\chi_{7056}(521, \cdot)$$ None 0 2
7056.2.cq $$\chi_{7056}(863, \cdot)$$ n/a 160 2
7056.2.cr $$\chi_{7056}(361, \cdot)$$ None 0 2
7056.2.cs $$\chi_{7056}(4735, \cdot)$$ n/a 200 2
7056.2.cx $$\chi_{7056}(3919, \cdot)$$ n/a 480 2
7056.2.cy $$\chi_{7056}(2137, \cdot)$$ None 0 2
7056.2.cz $$\chi_{7056}(607, \cdot)$$ n/a 480 2
7056.2.da $$\chi_{7056}(1177, \cdot)$$ None 0 2
7056.2.df $$\chi_{7056}(1697, \cdot)$$ n/a 472 2
7056.2.dg $$\chi_{7056}(2615, \cdot)$$ None 0 2
7056.2.dh $$\chi_{7056}(3559, \cdot)$$ None 0 2
7056.2.dk $$\chi_{7056}(1009, \cdot)$$ n/a 834 6
7056.2.dl $$\chi_{7056}(979, \cdot)$$ n/a 3808 4
7056.2.dn $$\chi_{7056}(491, \cdot)$$ n/a 3896 4
7056.2.dp $$\chi_{7056}(949, \cdot)$$ n/a 3808 4
7056.2.ds $$\chi_{7056}(509, \cdot)$$ n/a 3808 4
7056.2.dt $$\chi_{7056}(2285, \cdot)$$ n/a 1280 4
7056.2.dv $$\chi_{7056}(1549, \cdot)$$ n/a 1584 4
7056.2.dy $$\chi_{7056}(373, \cdot)$$ n/a 3808 4
7056.2.dz $$\chi_{7056}(1685, \cdot)$$ n/a 3808 4
7056.2.eb $$\chi_{7056}(851, \cdot)$$ n/a 3808 4
7056.2.ed $$\chi_{7056}(19, \cdot)$$ n/a 1584 4
7056.2.eg $$\chi_{7056}(619, \cdot)$$ n/a 3808 4
7056.2.ei $$\chi_{7056}(275, \cdot)$$ n/a 3808 4
7056.2.ej $$\chi_{7056}(2627, \cdot)$$ n/a 1280 4
7056.2.el $$\chi_{7056}(1195, \cdot)$$ n/a 3808 4
7056.2.en $$\chi_{7056}(293, \cdot)$$ n/a 3808 4
7056.2.ep $$\chi_{7056}(589, \cdot)$$ n/a 3896 4
7056.2.er $$\chi_{7056}(55, \cdot)$$ None 0 6
7056.2.ew $$\chi_{7056}(1889, \cdot)$$ n/a 672 6
7056.2.ex $$\chi_{7056}(71, \cdot)$$ None 0 6
7056.2.ey $$\chi_{7056}(377, \cdot)$$ None 0 6
7056.2.ez $$\chi_{7056}(575, \cdot)$$ n/a 672 6
7056.2.fe $$\chi_{7056}(505, \cdot)$$ None 0 6
7056.2.ff $$\chi_{7056}(559, \cdot)$$ n/a 840 6
7056.2.fg $$\chi_{7056}(193, \cdot)$$ n/a 4008 12
7056.2.fh $$\chi_{7056}(289, \cdot)$$ n/a 1668 12
7056.2.fi $$\chi_{7056}(337, \cdot)$$ n/a 4008 12
7056.2.fj $$\chi_{7056}(529, \cdot)$$ n/a 4008 12
7056.2.fk $$\chi_{7056}(125, \cdot)$$ n/a 5376 12
7056.2.fm $$\chi_{7056}(253, \cdot)$$ n/a 6696 12
7056.2.fo $$\chi_{7056}(307, \cdot)$$ n/a 6696 12
7056.2.fq $$\chi_{7056}(323, \cdot)$$ n/a 5376 12
7056.2.fu $$\chi_{7056}(439, \cdot)$$ None 0 12
7056.2.fv $$\chi_{7056}(599, \cdot)$$ None 0 12
7056.2.fw $$\chi_{7056}(689, \cdot)$$ n/a 4008 12
7056.2.gb $$\chi_{7056}(169, \cdot)$$ None 0 12
7056.2.gc $$\chi_{7056}(367, \cdot)$$ n/a 4032 12
7056.2.gd $$\chi_{7056}(25, \cdot)$$ None 0 12
7056.2.ge $$\chi_{7056}(223, \cdot)$$ n/a 4032 12
7056.2.gj $$\chi_{7056}(271, \cdot)$$ n/a 1680 12
7056.2.gk $$\chi_{7056}(793, \cdot)$$ None 0 12
7056.2.gl $$\chi_{7056}(431, \cdot)$$ n/a 1344 12
7056.2.gm $$\chi_{7056}(89, \cdot)$$ None 0 12
7056.2.gr $$\chi_{7056}(41, \cdot)$$ None 0 12
7056.2.gs $$\chi_{7056}(527, \cdot)$$ n/a 4032 12
7056.2.gt $$\chi_{7056}(761, \cdot)$$ None 0 12
7056.2.gu $$\chi_{7056}(239, \cdot)$$ n/a 4032 12
7056.2.gz $$\chi_{7056}(209, \cdot)$$ n/a 4008 12
7056.2.ha $$\chi_{7056}(23, \cdot)$$ None 0 12
7056.2.hb $$\chi_{7056}(257, \cdot)$$ n/a 4008 12
7056.2.hc $$\chi_{7056}(407, \cdot)$$ None 0 12
7056.2.hh $$\chi_{7056}(359, \cdot)$$ None 0 12
7056.2.hi $$\chi_{7056}(17, \cdot)$$ n/a 1344 12
7056.2.hj $$\chi_{7056}(199, \cdot)$$ None 0 12
7056.2.ho $$\chi_{7056}(103, \cdot)$$ None 0 12
7056.2.hp $$\chi_{7056}(727, \cdot)$$ None 0 12
7056.2.hu $$\chi_{7056}(95, \cdot)$$ n/a 4032 12
7056.2.hv $$\chi_{7056}(185, \cdot)$$ None 0 12
7056.2.hw $$\chi_{7056}(943, \cdot)$$ n/a 4032 12
7056.2.hx $$\chi_{7056}(457, \cdot)$$ None 0 12
7056.2.ib $$\chi_{7056}(85, \cdot)$$ n/a 32160 24
7056.2.id $$\chi_{7056}(461, \cdot)$$ n/a 32160 24
7056.2.if $$\chi_{7056}(187, \cdot)$$ n/a 32160 24
7056.2.ig $$\chi_{7056}(11, \cdot)$$ n/a 32160 24
7056.2.ij $$\chi_{7056}(107, \cdot)$$ n/a 10752 24
7056.2.il $$\chi_{7056}(451, \cdot)$$ n/a 13392 24
7056.2.im $$\chi_{7056}(115, \cdot)$$ n/a 32160 24
7056.2.ip $$\chi_{7056}(347, \cdot)$$ n/a 32160 24
7056.2.ir $$\chi_{7056}(173, \cdot)$$ n/a 32160 24
7056.2.it $$\chi_{7056}(37, \cdot)$$ n/a 13392 24
7056.2.iu $$\chi_{7056}(277, \cdot)$$ n/a 32160 24
7056.2.iw $$\chi_{7056}(5, \cdot)$$ n/a 32160 24
7056.2.iz $$\chi_{7056}(269, \cdot)$$ n/a 10752 24
7056.2.jb $$\chi_{7056}(205, \cdot)$$ n/a 32160 24
7056.2.jd $$\chi_{7056}(155, \cdot)$$ n/a 32160 24
7056.2.jf $$\chi_{7056}(139, \cdot)$$ n/a 32160 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7056))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7056)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 45}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 27}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1008))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1764))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2352))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3528))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7056))$$$$^{\oplus 1}$$