Properties

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

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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 the 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

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