# Properties

 Label 6720.2 Level 6720 Weight 2 Dimension 435864 Nonzero newspaces 112 Sturm bound 4718592

## Defining parameters

 Level: $$N$$ = $$6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$112$$ Sturm bound: $$4718592$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6720))$$.

Total New Old
Modular forms 1193472 438504 754968
Cusp forms 1165825 435864 729961
Eisenstein series 27647 2640 25007

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6720))$$

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
6720.2.a $$\chi_{6720}(1, \cdot)$$ 6720.2.a.a 1 1
6720.2.a.b 1
6720.2.a.c 1
6720.2.a.d 1
6720.2.a.e 1
6720.2.a.f 1
6720.2.a.g 1
6720.2.a.h 1
6720.2.a.i 1
6720.2.a.j 1
6720.2.a.k 1
6720.2.a.l 1
6720.2.a.m 1
6720.2.a.n 1
6720.2.a.o 1
6720.2.a.p 1
6720.2.a.q 1
6720.2.a.r 1
6720.2.a.s 1
6720.2.a.t 1
6720.2.a.u 1
6720.2.a.v 1
6720.2.a.w 1
6720.2.a.x 1
6720.2.a.y 1
6720.2.a.z 1
6720.2.a.ba 1
6720.2.a.bb 1
6720.2.a.bc 1
6720.2.a.bd 1
6720.2.a.be 1
6720.2.a.bf 1
6720.2.a.bg 1
6720.2.a.bh 1
6720.2.a.bi 1
6720.2.a.bj 1
6720.2.a.bk 1
6720.2.a.bl 1
6720.2.a.bm 1
6720.2.a.bn 1
6720.2.a.bo 1
6720.2.a.bp 1
6720.2.a.bq 1
6720.2.a.br 1
6720.2.a.bs 1
6720.2.a.bt 1
6720.2.a.bu 1
6720.2.a.bv 1
6720.2.a.bw 1
6720.2.a.bx 1
6720.2.a.by 1
6720.2.a.bz 1
6720.2.a.ca 1
6720.2.a.cb 1
6720.2.a.cc 1
6720.2.a.cd 1
6720.2.a.ce 1
6720.2.a.cf 1
6720.2.a.cg 1
6720.2.a.ch 1
6720.2.a.ci 1
6720.2.a.cj 1
6720.2.a.ck 1
6720.2.a.cl 1
6720.2.a.cm 1
6720.2.a.cn 1
6720.2.a.co 2
6720.2.a.cp 2
6720.2.a.cq 2
6720.2.a.cr 2
6720.2.a.cs 2
6720.2.a.ct 2
6720.2.a.cu 2
6720.2.a.cv 2
6720.2.a.cw 2
6720.2.a.cx 2
6720.2.a.cy 2
6720.2.a.cz 2
6720.2.a.da 3
6720.2.a.db 3
6720.2.d $$\chi_{6720}(6271, \cdot)$$ n/a 128 1
6720.2.e $$\chi_{6720}(2591, \cdot)$$ n/a 192 1
6720.2.f $$\chi_{6720}(2561, \cdot)$$ n/a 256 1
6720.2.g $$\chi_{6720}(3361, \cdot)$$ 6720.2.g.a 2 1
6720.2.g.b 2
6720.2.g.c 2
6720.2.g.d 2
6720.2.g.e 2
6720.2.g.f 2
6720.2.g.g 2
6720.2.g.h 2
6720.2.g.i 4
6720.2.g.j 4
6720.2.g.k 4
6720.2.g.l 4
6720.2.g.m 8
6720.2.g.n 8
6720.2.g.o 8
6720.2.g.p 8
6720.2.g.q 8
6720.2.g.r 8
6720.2.g.s 8
6720.2.g.t 8
6720.2.j $$\chi_{6720}(6049, \cdot)$$ n/a 144 1
6720.2.k $$\chi_{6720}(5249, \cdot)$$ n/a 376 1
6720.2.p $$\chi_{6720}(5279, \cdot)$$ n/a 288 1
6720.2.q $$\chi_{6720}(2239, \cdot)$$ n/a 192 1
6720.2.t $$\chi_{6720}(2689, \cdot)$$ n/a 144 1
6720.2.u $$\chi_{6720}(1889, \cdot)$$ n/a 384 1
6720.2.v $$\chi_{6720}(1919, \cdot)$$ n/a 288 1
6720.2.w $$\chi_{6720}(5599, \cdot)$$ n/a 192 1
6720.2.z $$\chi_{6720}(2911, \cdot)$$ n/a 128 1
6720.2.ba $$\chi_{6720}(5951, \cdot)$$ n/a 192 1
6720.2.bf $$\chi_{6720}(5921, \cdot)$$ n/a 256 1
6720.2.bg $$\chi_{6720}(961, \cdot)$$ n/a 256 2
6720.2.bj $$\chi_{6720}(97, \cdot)$$ n/a 384 2
6720.2.bk $$\chi_{6720}(1793, \cdot)$$ n/a 576 2
6720.2.bl $$\chi_{6720}(127, \cdot)$$ n/a 288 2
6720.2.bm $$\chi_{6720}(4703, \cdot)$$ n/a 768 2
6720.2.bp $$\chi_{6720}(1807, \cdot)$$ n/a 288 2
6720.2.bs $$\chi_{6720}(433, \cdot)$$ n/a 384 2
6720.2.bu $$\chi_{6720}(1457, \cdot)$$ n/a 576 2
6720.2.bv $$\chi_{6720}(1007, \cdot)$$ n/a 752 2
6720.2.bx $$\chi_{6720}(209, \cdot)$$ n/a 752 2
6720.2.ca $$\chi_{6720}(911, \cdot)$$ n/a 384 2
6720.2.cb $$\chi_{6720}(1009, \cdot)$$ n/a 288 2
6720.2.ce $$\chi_{6720}(1231, \cdot)$$ n/a 256 2
6720.2.cg $$\chi_{6720}(1681, \cdot)$$ n/a 192 2
6720.2.ch $$\chi_{6720}(559, \cdot)$$ n/a 384 2
6720.2.ck $$\chi_{6720}(881, \cdot)$$ n/a 512 2
6720.2.cl $$\chi_{6720}(239, \cdot)$$ n/a 576 2
6720.2.co $$\chi_{6720}(1777, \cdot)$$ n/a 384 2
6720.2.cp $$\chi_{6720}(463, \cdot)$$ n/a 288 2
6720.2.cr $$\chi_{6720}(4367, \cdot)$$ n/a 752 2
6720.2.cu $$\chi_{6720}(113, \cdot)$$ n/a 576 2
6720.2.cx $$\chi_{6720}(2143, \cdot)$$ n/a 288 2
6720.2.cy $$\chi_{6720}(1343, \cdot)$$ n/a 752 2
6720.2.cz $$\chi_{6720}(2113, \cdot)$$ n/a 384 2
6720.2.da $$\chi_{6720}(5153, \cdot)$$ n/a 576 2
6720.2.df $$\chi_{6720}(2719, \cdot)$$ n/a 384 2
6720.2.dg $$\chi_{6720}(2879, \cdot)$$ n/a 752 2
6720.2.dh $$\chi_{6720}(929, \cdot)$$ n/a 768 2
6720.2.di $$\chi_{6720}(3649, \cdot)$$ n/a 384 2
6720.2.dl $$\chi_{6720}(3041, \cdot)$$ n/a 512 2
6720.2.dq $$\chi_{6720}(191, \cdot)$$ n/a 512 2
6720.2.dr $$\chi_{6720}(31, \cdot)$$ n/a 256 2
6720.2.du $$\chi_{6720}(4321, \cdot)$$ n/a 256 2
6720.2.dv $$\chi_{6720}(1601, \cdot)$$ n/a 512 2
6720.2.dw $$\chi_{6720}(3551, \cdot)$$ n/a 512 2
6720.2.dx $$\chi_{6720}(3391, \cdot)$$ n/a 256 2
6720.2.ea $$\chi_{6720}(1279, \cdot)$$ n/a 384 2
6720.2.eb $$\chi_{6720}(1439, \cdot)$$ n/a 768 2
6720.2.eg $$\chi_{6720}(2369, \cdot)$$ n/a 752 2
6720.2.eh $$\chi_{6720}(289, \cdot)$$ n/a 384 2
6720.2.ei $$\chi_{6720}(41, \cdot)$$ None 0 4
6720.2.ek $$\chi_{6720}(1079, \cdot)$$ None 0 4
6720.2.en $$\chi_{6720}(841, \cdot)$$ None 0 4
6720.2.ep $$\chi_{6720}(1399, \cdot)$$ None 0 4
6720.2.es $$\chi_{6720}(2647, \cdot)$$ None 0 4
6720.2.et $$\chi_{6720}(2617, \cdot)$$ None 0 4
6720.2.ew $$\chi_{6720}(167, \cdot)$$ None 0 4
6720.2.ex $$\chi_{6720}(617, \cdot)$$ None 0 4
6720.2.ey $$\chi_{6720}(967, \cdot)$$ None 0 4
6720.2.ez $$\chi_{6720}(937, \cdot)$$ None 0 4
6720.2.fc $$\chi_{6720}(1847, \cdot)$$ None 0 4
6720.2.fd $$\chi_{6720}(2297, \cdot)$$ None 0 4
6720.2.fh $$\chi_{6720}(71, \cdot)$$ None 0 4
6720.2.fj $$\chi_{6720}(1049, \cdot)$$ None 0 4
6720.2.fk $$\chi_{6720}(391, \cdot)$$ None 0 4
6720.2.fm $$\chi_{6720}(169, \cdot)$$ None 0 4
6720.2.fo $$\chi_{6720}(737, \cdot)$$ n/a 1536 4
6720.2.fp $$\chi_{6720}(577, \cdot)$$ n/a 768 4
6720.2.fu $$\chi_{6720}(383, \cdot)$$ n/a 1504 4
6720.2.fv $$\chi_{6720}(3103, \cdot)$$ n/a 768 4
6720.2.fw $$\chi_{6720}(47, \cdot)$$ n/a 1504 4
6720.2.fz $$\chi_{6720}(2417, \cdot)$$ n/a 1504 4
6720.2.gb $$\chi_{6720}(2257, \cdot)$$ n/a 768 4
6720.2.gc $$\chi_{6720}(2767, \cdot)$$ n/a 768 4
6720.2.ge $$\chi_{6720}(1361, \cdot)$$ n/a 1024 4
6720.2.gh $$\chi_{6720}(1199, \cdot)$$ n/a 1504 4
6720.2.gi $$\chi_{6720}(1201, \cdot)$$ n/a 512 4
6720.2.gl $$\chi_{6720}(1039, \cdot)$$ n/a 768 4
6720.2.gn $$\chi_{6720}(529, \cdot)$$ n/a 768 4
6720.2.go $$\chi_{6720}(271, \cdot)$$ n/a 512 4
6720.2.gr $$\chi_{6720}(689, \cdot)$$ n/a 1504 4
6720.2.gs $$\chi_{6720}(431, \cdot)$$ n/a 1024 4
6720.2.gv $$\chi_{6720}(977, \cdot)$$ n/a 1504 4
6720.2.gw $$\chi_{6720}(1487, \cdot)$$ n/a 1504 4
6720.2.gy $$\chi_{6720}(1327, \cdot)$$ n/a 768 4
6720.2.hb $$\chi_{6720}(817, \cdot)$$ n/a 768 4
6720.2.hc $$\chi_{6720}(1823, \cdot)$$ n/a 1536 4
6720.2.hd $$\chi_{6720}(1087, \cdot)$$ n/a 768 4
6720.2.hi $$\chi_{6720}(2753, \cdot)$$ n/a 1504 4
6720.2.hj $$\chi_{6720}(2593, \cdot)$$ n/a 768 4
6720.2.hk $$\chi_{6720}(197, \cdot)$$ n/a 9216 8
6720.2.hn $$\chi_{6720}(923, \cdot)$$ n/a 12224 8
6720.2.hp $$\chi_{6720}(13, \cdot)$$ n/a 6144 8
6720.2.hq $$\chi_{6720}(43, \cdot)$$ n/a 4608 8
6720.2.hs $$\chi_{6720}(139, \cdot)$$ n/a 6144 8
6720.2.hv $$\chi_{6720}(421, \cdot)$$ n/a 3072 8
6720.2.hx $$\chi_{6720}(811, \cdot)$$ n/a 4096 8
6720.2.hy $$\chi_{6720}(589, \cdot)$$ n/a 4608 8
6720.2.ia $$\chi_{6720}(629, \cdot)$$ n/a 12224 8
6720.2.id $$\chi_{6720}(491, \cdot)$$ n/a 6144 8
6720.2.if $$\chi_{6720}(461, \cdot)$$ n/a 8192 8
6720.2.ig $$\chi_{6720}(659, \cdot)$$ n/a 9216 8
6720.2.ij $$\chi_{6720}(83, \cdot)$$ n/a 12224 8
6720.2.ik $$\chi_{6720}(533, \cdot)$$ n/a 9216 8
6720.2.im $$\chi_{6720}(883, \cdot)$$ n/a 4608 8
6720.2.ip $$\chi_{6720}(853, \cdot)$$ n/a 6144 8
6720.2.iq $$\chi_{6720}(1129, \cdot)$$ None 0 8
6720.2.is $$\chi_{6720}(871, \cdot)$$ None 0 8
6720.2.iv $$\chi_{6720}(89, \cdot)$$ None 0 8
6720.2.ix $$\chi_{6720}(1031, \cdot)$$ None 0 8
6720.2.ja $$\chi_{6720}(233, \cdot)$$ None 0 8
6720.2.jb $$\chi_{6720}(887, \cdot)$$ None 0 8
6720.2.je $$\chi_{6720}(313, \cdot)$$ None 0 8
6720.2.jf $$\chi_{6720}(487, \cdot)$$ None 0 8
6720.2.jg $$\chi_{6720}(137, \cdot)$$ None 0 8
6720.2.jh $$\chi_{6720}(647, \cdot)$$ None 0 8
6720.2.jk $$\chi_{6720}(73, \cdot)$$ None 0 8
6720.2.jl $$\chi_{6720}(247, \cdot)$$ None 0 8
6720.2.jp $$\chi_{6720}(199, \cdot)$$ None 0 8
6720.2.jr $$\chi_{6720}(121, \cdot)$$ None 0 8
6720.2.js $$\chi_{6720}(359, \cdot)$$ None 0 8
6720.2.ju $$\chi_{6720}(521, \cdot)$$ None 0 8
6720.2.jw $$\chi_{6720}(157, \cdot)$$ n/a 12288 16
6720.2.jz $$\chi_{6720}(163, \cdot)$$ n/a 12288 16
6720.2.kb $$\chi_{6720}(53, \cdot)$$ n/a 24448 16
6720.2.kc $$\chi_{6720}(563, \cdot)$$ n/a 24448 16
6720.2.ke $$\chi_{6720}(11, \cdot)$$ n/a 16384 16
6720.2.kh $$\chi_{6720}(269, \cdot)$$ n/a 24448 16
6720.2.kj $$\chi_{6720}(179, \cdot)$$ n/a 24448 16
6720.2.kk $$\chi_{6720}(101, \cdot)$$ n/a 16384 16
6720.2.km $$\chi_{6720}(541, \cdot)$$ n/a 8192 16
6720.2.kp $$\chi_{6720}(19, \cdot)$$ n/a 12288 16
6720.2.kr $$\chi_{6720}(109, \cdot)$$ n/a 12288 16
6720.2.ks $$\chi_{6720}(451, \cdot)$$ n/a 8192 16
6720.2.kv $$\chi_{6720}(67, \cdot)$$ n/a 12288 16
6720.2.kw $$\chi_{6720}(493, \cdot)$$ n/a 12288 16
6720.2.ky $$\chi_{6720}(227, \cdot)$$ n/a 24448 16
6720.2.lb $$\chi_{6720}(653, \cdot)$$ n/a 24448 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6720))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6720)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 56}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(480))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(672))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(840))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(960))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1344))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1680))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6720))$$$$^{\oplus 1}$$