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Properties

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

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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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(6336)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 42}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1056))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6336))\)\(^{\oplus 1}\)