# Properties

 Label 6336.2 Level 6336 Weight 2 Dimension 482490 Nonzero newspaces 64 Sturm bound 4423680

## Defining parameters

 Level: $$N$$ = $$6336 = 2^{6} \cdot 3^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$4423680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6336))$$.

Total New Old
Modular forms 1117440 486054 631386
Cusp forms 1094401 482490 611911
Eisenstein series 23039 3564 19475

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6336))$$

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
6336.2.a $$\chi_{6336}(1, \cdot)$$ 6336.2.a.a 1 1
6336.2.a.b 1
6336.2.a.c 1
6336.2.a.d 1
6336.2.a.e 1
6336.2.a.f 1
6336.2.a.g 1
6336.2.a.h 1
6336.2.a.i 1
6336.2.a.j 1
6336.2.a.k 1
6336.2.a.l 1
6336.2.a.m 1
6336.2.a.n 1
6336.2.a.o 1
6336.2.a.p 1
6336.2.a.q 1
6336.2.a.r 1
6336.2.a.s 1
6336.2.a.t 1
6336.2.a.u 1
6336.2.a.v 1
6336.2.a.w 1
6336.2.a.x 1
6336.2.a.y 1
6336.2.a.z 1
6336.2.a.ba 1
6336.2.a.bb 1
6336.2.a.bc 1
6336.2.a.bd 1
6336.2.a.be 1
6336.2.a.bf 1
6336.2.a.bg 1
6336.2.a.bh 1
6336.2.a.bi 1
6336.2.a.bj 1
6336.2.a.bk 1
6336.2.a.bl 1
6336.2.a.bm 1
6336.2.a.bn 1
6336.2.a.bo 1
6336.2.a.bp 1
6336.2.a.bq 1
6336.2.a.br 1
6336.2.a.bs 1
6336.2.a.bt 1
6336.2.a.bu 1
6336.2.a.bv 1
6336.2.a.bw 1
6336.2.a.bx 1
6336.2.a.by 1
6336.2.a.bz 1
6336.2.a.ca 1
6336.2.a.cb 1
6336.2.a.cc 1
6336.2.a.cd 1
6336.2.a.ce 1
6336.2.a.cf 1
6336.2.a.cg 1
6336.2.a.ch 1
6336.2.a.ci 1
6336.2.a.cj 1
6336.2.a.ck 1
6336.2.a.cl 1
6336.2.a.cm 1
6336.2.a.cn 1
6336.2.a.co 2
6336.2.a.cp 2
6336.2.a.cq 2
6336.2.a.cr 2
6336.2.a.cs 2
6336.2.a.ct 2
6336.2.a.cu 2
6336.2.a.cv 2
6336.2.a.cw 2
6336.2.a.cx 2
6336.2.a.cy 3
6336.2.a.cz 3
6336.2.a.da 4
6336.2.a.db 4
6336.2.b $$\chi_{6336}(2177, \cdot)$$ 6336.2.b.a 2 1
6336.2.b.b 2
6336.2.b.c 2
6336.2.b.d 2
6336.2.b.e 2
6336.2.b.f 2
6336.2.b.g 2
6336.2.b.h 2
6336.2.b.i 2
6336.2.b.j 2
6336.2.b.k 2
6336.2.b.l 2
6336.2.b.m 2
6336.2.b.n 2
6336.2.b.o 2
6336.2.b.p 2
6336.2.b.q 4
6336.2.b.r 4
6336.2.b.s 4
6336.2.b.t 4
6336.2.b.u 4
6336.2.b.v 4
6336.2.b.w 6
6336.2.b.x 6
6336.2.b.y 6
6336.2.b.z 6
6336.2.b.ba 8
6336.2.b.bb 8
6336.2.d $$\chi_{6336}(3455, \cdot)$$ 6336.2.d.a 2 1
6336.2.d.b 2
6336.2.d.c 8
6336.2.d.d 8
6336.2.d.e 8
6336.2.d.f 8
6336.2.d.g 10
6336.2.d.h 10
6336.2.d.i 12
6336.2.d.j 12
6336.2.f $$\chi_{6336}(3169, \cdot)$$ 6336.2.f.a 4 1
6336.2.f.b 4
6336.2.f.c 4
6336.2.f.d 4
6336.2.f.e 4
6336.2.f.f 4
6336.2.f.g 4
6336.2.f.h 4
6336.2.f.i 8
6336.2.f.j 8
6336.2.f.k 8
6336.2.f.l 8
6336.2.f.m 12
6336.2.f.n 12
6336.2.f.o 12
6336.2.h $$\chi_{6336}(3871, \cdot)$$ n/a 120 1
6336.2.k $$\chi_{6336}(287, \cdot)$$ 6336.2.k.a 4 1
6336.2.k.b 4
6336.2.k.c 12
6336.2.k.d 12
6336.2.k.e 24
6336.2.k.f 24
6336.2.m $$\chi_{6336}(5345, \cdot)$$ 6336.2.m.a 8 1
6336.2.m.b 8
6336.2.m.c 16
6336.2.m.d 16
6336.2.m.e 48
6336.2.o $$\chi_{6336}(703, \cdot)$$ n/a 118 1
6336.2.q $$\chi_{6336}(2113, \cdot)$$ n/a 480 2
6336.2.r $$\chi_{6336}(2287, \cdot)$$ n/a 236 2
6336.2.u $$\chi_{6336}(1585, \cdot)$$ n/a 200 2
6336.2.v $$\chi_{6336}(1871, \cdot)$$ n/a 160 2
6336.2.y $$\chi_{6336}(593, \cdot)$$ n/a 192 2
6336.2.z $$\chi_{6336}(577, \cdot)$$ n/a 472 4
6336.2.bc $$\chi_{6336}(2815, \cdot)$$ n/a 568 2
6336.2.be $$\chi_{6336}(1121, \cdot)$$ n/a 576 2
6336.2.bg $$\chi_{6336}(2399, \cdot)$$ n/a 480 2
6336.2.bh $$\chi_{6336}(1759, \cdot)$$ n/a 576 2
6336.2.bj $$\chi_{6336}(1057, \cdot)$$ n/a 480 2
6336.2.bl $$\chi_{6336}(1343, \cdot)$$ n/a 480 2
6336.2.bn $$\chi_{6336}(65, \cdot)$$ n/a 568 2
6336.2.br $$\chi_{6336}(793, \cdot)$$ None 0 4
6336.2.bs $$\chi_{6336}(1385, \cdot)$$ None 0 4
6336.2.bt $$\chi_{6336}(1079, \cdot)$$ None 0 4
6336.2.bu $$\chi_{6336}(1495, \cdot)$$ None 0 4
6336.2.by $$\chi_{6336}(127, \cdot)$$ n/a 472 4
6336.2.ca $$\chi_{6336}(161, \cdot)$$ n/a 384 4
6336.2.cc $$\chi_{6336}(863, \cdot)$$ n/a 384 4
6336.2.cf $$\chi_{6336}(415, \cdot)$$ n/a 480 4
6336.2.ch $$\chi_{6336}(289, \cdot)$$ n/a 480 4
6336.2.cj $$\chi_{6336}(575, \cdot)$$ n/a 384 4
6336.2.cl $$\chi_{6336}(1025, \cdot)$$ n/a 384 4
6336.2.cn $$\chi_{6336}(815, \cdot)$$ n/a 960 4
6336.2.co $$\chi_{6336}(1649, \cdot)$$ n/a 1136 4
6336.2.cr $$\chi_{6336}(175, \cdot)$$ n/a 1136 4
6336.2.cs $$\chi_{6336}(529, \cdot)$$ n/a 960 4
6336.2.cu $$\chi_{6336}(961, \cdot)$$ n/a 2272 8
6336.2.cx $$\chi_{6336}(197, \cdot)$$ n/a 3072 8
6336.2.cy $$\chi_{6336}(397, \cdot)$$ n/a 3200 8
6336.2.cz $$\chi_{6336}(683, \cdot)$$ n/a 2560 8
6336.2.da $$\chi_{6336}(307, \cdot)$$ n/a 3824 8
6336.2.dd $$\chi_{6336}(17, \cdot)$$ n/a 768 8
6336.2.dg $$\chi_{6336}(719, \cdot)$$ n/a 768 8
6336.2.dh $$\chi_{6336}(433, \cdot)$$ n/a 944 8
6336.2.dk $$\chi_{6336}(271, \cdot)$$ n/a 944 8
6336.2.dl $$\chi_{6336}(329, \cdot)$$ None 0 8
6336.2.dm $$\chi_{6336}(265, \cdot)$$ None 0 8
6336.2.dr $$\chi_{6336}(439, \cdot)$$ None 0 8
6336.2.ds $$\chi_{6336}(23, \cdot)$$ None 0 8
6336.2.du $$\chi_{6336}(833, \cdot)$$ n/a 2272 8
6336.2.dw $$\chi_{6336}(191, \cdot)$$ n/a 2272 8
6336.2.dy $$\chi_{6336}(97, \cdot)$$ n/a 2304 8
6336.2.ea $$\chi_{6336}(607, \cdot)$$ n/a 2304 8
6336.2.eb $$\chi_{6336}(1247, \cdot)$$ n/a 2304 8
6336.2.ed $$\chi_{6336}(545, \cdot)$$ n/a 2304 8
6336.2.ef $$\chi_{6336}(1471, \cdot)$$ n/a 2272 8
6336.2.ek $$\chi_{6336}(343, \cdot)$$ None 0 16
6336.2.el $$\chi_{6336}(71, \cdot)$$ None 0 16
6336.2.em $$\chi_{6336}(233, \cdot)$$ None 0 16
6336.2.en $$\chi_{6336}(361, \cdot)$$ None 0 16
6336.2.es $$\chi_{6336}(155, \cdot)$$ n/a 15360 16
6336.2.et $$\chi_{6336}(43, \cdot)$$ n/a 18368 16
6336.2.eu $$\chi_{6336}(461, \cdot)$$ n/a 18368 16
6336.2.ev $$\chi_{6336}(133, \cdot)$$ n/a 15360 16
6336.2.ez $$\chi_{6336}(49, \cdot)$$ n/a 4544 16
6336.2.fa $$\chi_{6336}(79, \cdot)$$ n/a 4544 16
6336.2.fd $$\chi_{6336}(497, \cdot)$$ n/a 4544 16
6336.2.fe $$\chi_{6336}(47, \cdot)$$ n/a 4544 16
6336.2.fg $$\chi_{6336}(19, \cdot)$$ n/a 15296 32
6336.2.fh $$\chi_{6336}(179, \cdot)$$ n/a 12288 32
6336.2.fm $$\chi_{6336}(37, \cdot)$$ n/a 15296 32
6336.2.fn $$\chi_{6336}(413, \cdot)$$ n/a 12288 32
6336.2.fo $$\chi_{6336}(119, \cdot)$$ None 0 32
6336.2.fp $$\chi_{6336}(7, \cdot)$$ None 0 32
6336.2.fu $$\chi_{6336}(25, \cdot)$$ None 0 32
6336.2.fv $$\chi_{6336}(41, \cdot)$$ None 0 32
6336.2.fw $$\chi_{6336}(157, \cdot)$$ n/a 73472 64
6336.2.fx $$\chi_{6336}(29, \cdot)$$ n/a 73472 64
6336.2.gc $$\chi_{6336}(139, \cdot)$$ n/a 73472 64
6336.2.gd $$\chi_{6336}(59, \cdot)$$ n/a 73472 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6336))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6336)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 21}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(352))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(528))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(704))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(792))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1056))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1584))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3168))$$$$^{\oplus 2}$$