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Properties

Label 6800.2
Level 6800
Weight 2
Dimension 708944
Nonzero newspaces 100
Sturm bound 5529600

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Defining parameters

Level: \( N \) = \( 6800 = 2^{4} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(5529600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6800))\).

Total New Old
Modular forms 1394944 714478 680466
Cusp forms 1369857 708944 660913
Eisenstein series 25087 5534 19553

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6800))\)

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
6800.2.a \(\chi_{6800}(1, \cdot)\) 6800.2.a.a 1 1
6800.2.a.b 1
6800.2.a.c 1
6800.2.a.d 1
6800.2.a.e 1
6800.2.a.f 1
6800.2.a.g 1
6800.2.a.h 1
6800.2.a.i 1
6800.2.a.j 1
6800.2.a.k 1
6800.2.a.l 1
6800.2.a.m 1
6800.2.a.n 1
6800.2.a.o 1
6800.2.a.p 1
6800.2.a.q 1
6800.2.a.r 1
6800.2.a.s 1
6800.2.a.t 1
6800.2.a.u 1
6800.2.a.v 1
6800.2.a.w 1
6800.2.a.x 1
6800.2.a.y 1
6800.2.a.z 1
6800.2.a.ba 2
6800.2.a.bb 2
6800.2.a.bc 2
6800.2.a.bd 2
6800.2.a.be 2
6800.2.a.bf 2
6800.2.a.bg 2
6800.2.a.bh 2
6800.2.a.bi 2
6800.2.a.bj 3
6800.2.a.bk 3
6800.2.a.bl 3
6800.2.a.bm 3
6800.2.a.bn 3
6800.2.a.bo 3
6800.2.a.bp 3
6800.2.a.bq 3
6800.2.a.br 3
6800.2.a.bs 3
6800.2.a.bt 4
6800.2.a.bu 4
6800.2.a.bv 4
6800.2.a.bw 4
6800.2.a.bx 5
6800.2.a.by 5
6800.2.a.bz 5
6800.2.a.ca 5
6800.2.a.cb 5
6800.2.a.cc 5
6800.2.a.cd 5
6800.2.a.ce 5
6800.2.a.cf 5
6800.2.a.cg 5
6800.2.a.ch 6
6800.2.a.ci 6
6800.2.c \(\chi_{6800}(5201, \cdot)\) n/a 168 1
6800.2.e \(\chi_{6800}(2449, \cdot)\) n/a 144 1
6800.2.f \(\chi_{6800}(3401, \cdot)\) None 0 1
6800.2.h \(\chi_{6800}(4249, \cdot)\) None 0 1
6800.2.j \(\chi_{6800}(5849, \cdot)\) None 0 1
6800.2.l \(\chi_{6800}(1801, \cdot)\) None 0 1
6800.2.o \(\chi_{6800}(849, \cdot)\) n/a 160 1
6800.2.q \(\chi_{6800}(1407, \cdot)\) n/a 324 2
6800.2.s \(\chi_{6800}(1101, \cdot)\) n/a 1356 2
6800.2.v \(\chi_{6800}(2107, \cdot)\) n/a 1288 2
6800.2.x \(\chi_{6800}(307, \cdot)\) n/a 1152 2
6800.2.z \(\chi_{6800}(149, \cdot)\) n/a 1288 2
6800.2.bb \(\chi_{6800}(1543, \cdot)\) None 0 2
6800.2.bc \(\chi_{6800}(2707, \cdot)\) n/a 1288 2
6800.2.bf \(\chi_{6800}(2549, \cdot)\) n/a 1288 2
6800.2.bg \(\chi_{6800}(1701, \cdot)\) n/a 1216 2
6800.2.bj \(\chi_{6800}(6107, \cdot)\) n/a 1288 2
6800.2.bk \(\chi_{6800}(407, \cdot)\) None 0 2
6800.2.bn \(\chi_{6800}(2143, \cdot)\) n/a 288 2
6800.2.bp \(\chi_{6800}(4849, \cdot)\) n/a 320 2
6800.2.bq \(\chi_{6800}(5801, \cdot)\) None 0 2
6800.2.bt \(\chi_{6800}(2401, \cdot)\) n/a 336 2
6800.2.bu \(\chi_{6800}(1449, \cdot)\) None 0 2
6800.2.bw \(\chi_{6800}(2007, \cdot)\) None 0 2
6800.2.bz \(\chi_{6800}(543, \cdot)\) n/a 324 2
6800.2.ca \(\chi_{6800}(6243, \cdot)\) n/a 1288 2
6800.2.cd \(\chi_{6800}(101, \cdot)\) n/a 1356 2
6800.2.ce \(\chi_{6800}(749, \cdot)\) n/a 1152 2
6800.2.ch \(\chi_{6800}(2843, \cdot)\) n/a 1288 2
6800.2.cj \(\chi_{6800}(1143, \cdot)\) None 0 2
6800.2.ck \(\chi_{6800}(3549, \cdot)\) n/a 1288 2
6800.2.cm \(\chi_{6800}(3707, \cdot)\) n/a 1152 2
6800.2.co \(\chi_{6800}(5507, \cdot)\) n/a 1288 2
6800.2.cr \(\chi_{6800}(701, \cdot)\) n/a 1356 2
6800.2.cs \(\chi_{6800}(1007, \cdot)\) n/a 324 2
6800.2.cu \(\chi_{6800}(1361, \cdot)\) n/a 960 4
6800.2.cw \(\chi_{6800}(43, \cdot)\) n/a 2576 4
6800.2.cx \(\chi_{6800}(801, \cdot)\) n/a 672 4
6800.2.da \(\chi_{6800}(3449, \cdot)\) None 0 4
6800.2.dc \(\chi_{6800}(1243, \cdot)\) n/a 2576 4
6800.2.de \(\chi_{6800}(1549, \cdot)\) n/a 2576 4
6800.2.df \(\chi_{6800}(501, \cdot)\) n/a 2712 4
6800.2.dh \(\chi_{6800}(2943, \cdot)\) n/a 648 4
6800.2.dk \(\chi_{6800}(943, \cdot)\) n/a 648 4
6800.2.dl \(\chi_{6800}(2807, \cdot)\) None 0 4
6800.2.do \(\chi_{6800}(807, \cdot)\) None 0 4
6800.2.dq \(\chi_{6800}(349, \cdot)\) n/a 2576 4
6800.2.dr \(\chi_{6800}(2501, \cdot)\) n/a 2712 4
6800.2.dt \(\chi_{6800}(1443, \cdot)\) n/a 2576 4
6800.2.dw \(\chi_{6800}(49, \cdot)\) n/a 640 4
6800.2.dx \(\chi_{6800}(1001, \cdot)\) None 0 4
6800.2.dz \(\chi_{6800}(1307, \cdot)\) n/a 2576 4
6800.2.ec \(\chi_{6800}(441, \cdot)\) None 0 4
6800.2.ee \(\chi_{6800}(409, \cdot)\) None 0 4
6800.2.eg \(\chi_{6800}(2209, \cdot)\) n/a 1072 4
6800.2.ei \(\chi_{6800}(1089, \cdot)\) n/a 960 4
6800.2.ek \(\chi_{6800}(1121, \cdot)\) n/a 1072 4
6800.2.en \(\chi_{6800}(169, \cdot)\) None 0 4
6800.2.ep \(\chi_{6800}(681, \cdot)\) None 0 4
6800.2.er \(\chi_{6800}(1451, \cdot)\) n/a 5424 8
6800.2.et \(\chi_{6800}(793, \cdot)\) None 0 8
6800.2.eu \(\chi_{6800}(657, \cdot)\) n/a 1280 8
6800.2.ew \(\chi_{6800}(499, \cdot)\) n/a 5152 8
6800.2.ez \(\chi_{6800}(957, \cdot)\) n/a 5152 8
6800.2.fa \(\chi_{6800}(1557, \cdot)\) n/a 5152 8
6800.2.fc \(\chi_{6800}(551, \cdot)\) None 0 8
6800.2.ff \(\chi_{6800}(351, \cdot)\) n/a 1368 8
6800.2.fh \(\chi_{6800}(1999, \cdot)\) n/a 1296 8
6800.2.fi \(\chi_{6800}(199, \cdot)\) None 0 8
6800.2.fl \(\chi_{6800}(1693, \cdot)\) n/a 5152 8
6800.2.fm \(\chi_{6800}(1093, \cdot)\) n/a 5152 8
6800.2.fo \(\chi_{6800}(99, \cdot)\) n/a 5152 8
6800.2.fq \(\chi_{6800}(193, \cdot)\) n/a 1280 8
6800.2.ft \(\chi_{6800}(57, \cdot)\) None 0 8
6800.2.fv \(\chi_{6800}(651, \cdot)\) n/a 5424 8
6800.2.fw \(\chi_{6800}(727, \cdot)\) None 0 8
6800.2.fy \(\chi_{6800}(421, \cdot)\) n/a 8608 8
6800.2.gb \(\chi_{6800}(67, \cdot)\) n/a 8608 8
6800.2.gd \(\chi_{6800}(987, \cdot)\) n/a 7680 8
6800.2.gf \(\chi_{6800}(829, \cdot)\) n/a 8608 8
6800.2.gh \(\chi_{6800}(863, \cdot)\) n/a 2160 8
6800.2.gi \(\chi_{6800}(667, \cdot)\) n/a 8608 8
6800.2.gl \(\chi_{6800}(341, \cdot)\) n/a 7680 8
6800.2.gm \(\chi_{6800}(509, \cdot)\) n/a 8608 8
6800.2.gp \(\chi_{6800}(523, \cdot)\) n/a 8608 8
6800.2.gq \(\chi_{6800}(1087, \cdot)\) n/a 2160 8
6800.2.gt \(\chi_{6800}(103, \cdot)\) None 0 8
6800.2.gv \(\chi_{6800}(89, \cdot)\) None 0 8
6800.2.gw \(\chi_{6800}(81, \cdot)\) n/a 2144 8
6800.2.gz \(\chi_{6800}(361, \cdot)\) None 0 8
6800.2.ha \(\chi_{6800}(769, \cdot)\) n/a 2144 8
6800.2.hc \(\chi_{6800}(783, \cdot)\) n/a 1920 8
6800.2.hf \(\chi_{6800}(1223, \cdot)\) None 0 8
6800.2.hg \(\chi_{6800}(123, \cdot)\) n/a 8608 8
6800.2.hj \(\chi_{6800}(69, \cdot)\) n/a 7680 8
6800.2.hk \(\chi_{6800}(781, \cdot)\) n/a 8608 8
6800.2.hn \(\chi_{6800}(803, \cdot)\) n/a 8608 8
6800.2.hp \(\chi_{6800}(47, \cdot)\) n/a 2160 8
6800.2.hq \(\chi_{6800}(429, \cdot)\) n/a 8608 8
6800.2.hs \(\chi_{6800}(1667, \cdot)\) n/a 7680 8
6800.2.hu \(\chi_{6800}(747, \cdot)\) n/a 8608 8
6800.2.hx \(\chi_{6800}(21, \cdot)\) n/a 8608 8
6800.2.hy \(\chi_{6800}(183, \cdot)\) None 0 8
6800.2.ib \(\chi_{6800}(427, \cdot)\) n/a 17216 16
6800.2.id \(\chi_{6800}(121, \cdot)\) None 0 16
6800.2.ie \(\chi_{6800}(529, \cdot)\) n/a 4288 16
6800.2.ih \(\chi_{6800}(83, \cdot)\) n/a 17216 16
6800.2.ij \(\chi_{6800}(621, \cdot)\) n/a 17216 16
6800.2.ik \(\chi_{6800}(389, \cdot)\) n/a 17216 16
6800.2.in \(\chi_{6800}(87, \cdot)\) None 0 16
6800.2.io \(\chi_{6800}(247, \cdot)\) None 0 16
6800.2.ir \(\chi_{6800}(127, \cdot)\) n/a 4320 16
6800.2.is \(\chi_{6800}(287, \cdot)\) n/a 4320 16
6800.2.iv \(\chi_{6800}(461, \cdot)\) n/a 17216 16
6800.2.iw \(\chi_{6800}(189, \cdot)\) n/a 17216 16
6800.2.iy \(\chi_{6800}(467, \cdot)\) n/a 17216 16
6800.2.ja \(\chi_{6800}(9, \cdot)\) None 0 16
6800.2.jd \(\chi_{6800}(161, \cdot)\) n/a 4288 16
6800.2.je \(\chi_{6800}(603, \cdot)\) n/a 17216 16
6800.2.jg \(\chi_{6800}(211, \cdot)\) n/a 34432 32
6800.2.ji \(\chi_{6800}(73, \cdot)\) None 0 32
6800.2.jl \(\chi_{6800}(97, \cdot)\) n/a 8576 32
6800.2.jn \(\chi_{6800}(619, \cdot)\) n/a 34432 32
6800.2.jp \(\chi_{6800}(133, \cdot)\) n/a 34432 32
6800.2.jq \(\chi_{6800}(37, \cdot)\) n/a 34432 32
6800.2.jt \(\chi_{6800}(39, \cdot)\) None 0 32
6800.2.ju \(\chi_{6800}(79, \cdot)\) n/a 8640 32
6800.2.jw \(\chi_{6800}(31, \cdot)\) n/a 8640 32
6800.2.jz \(\chi_{6800}(71, \cdot)\) None 0 32
6800.2.kb \(\chi_{6800}(173, \cdot)\) n/a 34432 32
6800.2.kc \(\chi_{6800}(453, \cdot)\) n/a 34432 32
6800.2.kf \(\chi_{6800}(139, \cdot)\) n/a 34432 32
6800.2.kh \(\chi_{6800}(177, \cdot)\) n/a 8576 32
6800.2.ki \(\chi_{6800}(313, \cdot)\) None 0 32
6800.2.kk \(\chi_{6800}(11, \cdot)\) n/a 34432 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(680))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1700))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3400))\)\(^{\oplus 2}\)