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Properties

Label 6006.2
Level 6006
Weight 2
Dimension 225271
Nonzero newspaces 120
Sturm bound 3870720

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Defining parameters

Level: \( N \) = \( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(3870720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6006))\).

Total New Old
Modular forms 979200 225271 753929
Cusp forms 956161 225271 730890
Eisenstein series 23039 0 23039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6006))\)

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
6006.2.a \(\chi_{6006}(1, \cdot)\) 6006.2.a.a 1 1
6006.2.a.b 1
6006.2.a.c 1
6006.2.a.d 1
6006.2.a.e 1
6006.2.a.f 1
6006.2.a.g 1
6006.2.a.h 1
6006.2.a.i 1
6006.2.a.j 1
6006.2.a.k 1
6006.2.a.l 1
6006.2.a.m 1
6006.2.a.n 1
6006.2.a.o 1
6006.2.a.p 1
6006.2.a.q 1
6006.2.a.r 1
6006.2.a.s 1
6006.2.a.t 1
6006.2.a.u 1
6006.2.a.v 1
6006.2.a.w 1
6006.2.a.x 1
6006.2.a.y 1
6006.2.a.z 1
6006.2.a.ba 1
6006.2.a.bb 1
6006.2.a.bc 1
6006.2.a.bd 1
6006.2.a.be 1
6006.2.a.bf 1
6006.2.a.bg 2
6006.2.a.bh 2
6006.2.a.bi 2
6006.2.a.bj 2
6006.2.a.bk 2
6006.2.a.bl 2
6006.2.a.bm 2
6006.2.a.bn 2
6006.2.a.bo 2
6006.2.a.bp 2
6006.2.a.bq 3
6006.2.a.br 3
6006.2.a.bs 3
6006.2.a.bt 3
6006.2.a.bu 3
6006.2.a.bv 3
6006.2.a.bw 4
6006.2.a.bx 4
6006.2.a.by 4
6006.2.a.bz 4
6006.2.a.ca 4
6006.2.a.cb 4
6006.2.a.cc 4
6006.2.a.cd 4
6006.2.a.ce 4
6006.2.a.cf 6
6006.2.a.cg 7
6006.2.f \(\chi_{6006}(5279, \cdot)\) n/a 288 1
6006.2.g \(\chi_{6006}(4159, \cdot)\) n/a 144 1
6006.2.h \(\chi_{6006}(2729, \cdot)\) n/a 368 1
6006.2.i \(\chi_{6006}(5851, \cdot)\) n/a 192 1
6006.2.n \(\chi_{6006}(4577, \cdot)\) n/a 320 1
6006.2.o \(\chi_{6006}(4003, \cdot)\) n/a 224 1
6006.2.p \(\chi_{6006}(3431, \cdot)\) n/a 336 1
6006.2.q \(\chi_{6006}(1717, \cdot)\) n/a 320 2
6006.2.r \(\chi_{6006}(991, \cdot)\) n/a 376 2
6006.2.s \(\chi_{6006}(529, \cdot)\) n/a 376 2
6006.2.t \(\chi_{6006}(1387, \cdot)\) n/a 272 2
6006.2.y \(\chi_{6006}(967, \cdot)\) n/a 336 2
6006.2.z \(\chi_{6006}(265, \cdot)\) n/a 384 2
6006.2.ba \(\chi_{6006}(2465, \cdot)\) n/a 560 2
6006.2.bb \(\chi_{6006}(2309, \cdot)\) n/a 896 2
6006.2.bc \(\chi_{6006}(1093, \cdot)\) n/a 576 4
6006.2.bd \(\chi_{6006}(1231, \cdot)\) n/a 448 2
6006.2.be \(\chi_{6006}(881, \cdot)\) n/a 752 2
6006.2.bf \(\chi_{6006}(2311, \cdot)\) n/a 288 2
6006.2.bg \(\chi_{6006}(659, \cdot)\) n/a 672 2
6006.2.bp \(\chi_{6006}(901, \cdot)\) n/a 448 2
6006.2.bq \(\chi_{6006}(1277, \cdot)\) n/a 744 2
6006.2.br \(\chi_{6006}(2573, \cdot)\) n/a 896 2
6006.2.bs \(\chi_{6006}(2287, \cdot)\) n/a 448 2
6006.2.bt \(\chi_{6006}(2861, \cdot)\) n/a 640 2
6006.2.bu \(\chi_{6006}(725, \cdot)\) n/a 896 2
6006.2.cd \(\chi_{6006}(1187, \cdot)\) n/a 896 2
6006.2.ce \(\chi_{6006}(815, \cdot)\) n/a 744 2
6006.2.cf \(\chi_{6006}(439, \cdot)\) n/a 448 2
6006.2.ck \(\chi_{6006}(1453, \cdot)\) n/a 376 2
6006.2.cl \(\chi_{6006}(263, \cdot)\) n/a 896 2
6006.2.cm \(\chi_{6006}(703, \cdot)\) n/a 384 2
6006.2.cn \(\chi_{6006}(1013, \cdot)\) n/a 752 2
6006.2.co \(\chi_{6006}(3301, \cdot)\) n/a 368 2
6006.2.cp \(\chi_{6006}(989, \cdot)\) n/a 768 2
6006.2.cq \(\chi_{6006}(2551, \cdot)\) n/a 448 2
6006.2.cr \(\chi_{6006}(1739, \cdot)\) n/a 744 2
6006.2.da \(\chi_{6006}(2201, \cdot)\) n/a 744 2
6006.2.db \(\chi_{6006}(2089, \cdot)\) n/a 448 2
6006.2.dc \(\chi_{6006}(2837, \cdot)\) n/a 896 2
6006.2.dd \(\chi_{6006}(1915, \cdot)\) n/a 376 2
6006.2.de \(\chi_{6006}(1583, \cdot)\) n/a 672 2
6006.2.df \(\chi_{6006}(2155, \cdot)\) n/a 448 2
6006.2.dg \(\chi_{6006}(419, \cdot)\) n/a 752 2
6006.2.dl \(\chi_{6006}(701, \cdot)\) n/a 1344 4
6006.2.dm \(\chi_{6006}(1301, \cdot)\) n/a 1536 4
6006.2.dn \(\chi_{6006}(1273, \cdot)\) n/a 896 4
6006.2.ds \(\chi_{6006}(1637, \cdot)\) n/a 1792 4
6006.2.dt \(\chi_{6006}(391, \cdot)\) n/a 768 4
6006.2.du \(\chi_{6006}(365, \cdot)\) n/a 1152 4
6006.2.dv \(\chi_{6006}(883, \cdot)\) n/a 672 4
6006.2.ee \(\chi_{6006}(461, \cdot)\) n/a 1792 4
6006.2.ef \(\chi_{6006}(617, \cdot)\) n/a 1120 4
6006.2.eg \(\chi_{6006}(1409, \cdot)\) n/a 1504 4
6006.2.eh \(\chi_{6006}(3629, \cdot)\) n/a 1792 4
6006.2.ei \(\chi_{6006}(2069, \cdot)\) n/a 1488 4
6006.2.ej \(\chi_{6006}(395, \cdot)\) n/a 1792 4
6006.2.ek \(\chi_{6006}(1189, \cdot)\) n/a 736 4
6006.2.el \(\chi_{6006}(505, \cdot)\) n/a 672 4
6006.2.em \(\chi_{6006}(109, \cdot)\) n/a 896 4
6006.2.en \(\chi_{6006}(397, \cdot)\) n/a 752 4
6006.2.eo \(\chi_{6006}(3343, \cdot)\) n/a 896 4
6006.2.ep \(\chi_{6006}(1123, \cdot)\) n/a 736 4
6006.2.fc \(\chi_{6006}(1783, \cdot)\) n/a 752 4
6006.2.fd \(\chi_{6006}(1033, \cdot)\) n/a 896 4
6006.2.fe \(\chi_{6006}(1055, \cdot)\) n/a 1792 4
6006.2.ff \(\chi_{6006}(683, \cdot)\) n/a 1488 4
6006.2.fg \(\chi_{6006}(295, \cdot)\) n/a 1344 8
6006.2.fh \(\chi_{6006}(289, \cdot)\) n/a 1792 8
6006.2.fi \(\chi_{6006}(445, \cdot)\) n/a 1792 8
6006.2.fj \(\chi_{6006}(235, \cdot)\) n/a 1536 8
6006.2.fk \(\chi_{6006}(1357, \cdot)\) n/a 1792 8
6006.2.fl \(\chi_{6006}(1009, \cdot)\) n/a 1344 8
6006.2.fm \(\chi_{6006}(83, \cdot)\) n/a 3584 8
6006.2.fn \(\chi_{6006}(785, \cdot)\) n/a 2688 8
6006.2.fw \(\chi_{6006}(1063, \cdot)\) n/a 1792 8
6006.2.fx \(\chi_{6006}(1049, \cdot)\) n/a 3584 8
6006.2.fy \(\chi_{6006}(491, \cdot)\) n/a 2688 8
6006.2.fz \(\chi_{6006}(107, \cdot)\) n/a 3584 8
6006.2.ga \(\chi_{6006}(751, \cdot)\) n/a 1792 8
6006.2.gb \(\chi_{6006}(257, \cdot)\) n/a 3584 8
6006.2.gc \(\chi_{6006}(523, \cdot)\) n/a 1792 8
6006.2.gl \(\chi_{6006}(61, \cdot)\) n/a 1792 8
6006.2.gm \(\chi_{6006}(647, \cdot)\) n/a 3584 8
6006.2.gn \(\chi_{6006}(25, \cdot)\) n/a 1792 8
6006.2.go \(\chi_{6006}(1535, \cdot)\) n/a 3072 8
6006.2.gp \(\chi_{6006}(1249, \cdot)\) n/a 1536 8
6006.2.gq \(\chi_{6006}(311, \cdot)\) n/a 3584 8
6006.2.gr \(\chi_{6006}(361, \cdot)\) n/a 1792 8
6006.2.gs \(\chi_{6006}(809, \cdot)\) n/a 3584 8
6006.2.gx \(\chi_{6006}(269, \cdot)\) n/a 3584 8
6006.2.gy \(\chi_{6006}(745, \cdot)\) n/a 1792 8
6006.2.gz \(\chi_{6006}(95, \cdot)\) n/a 3584 8
6006.2.hi \(\chi_{6006}(1031, \cdot)\) n/a 3584 8
6006.2.hj \(\chi_{6006}(1195, \cdot)\) n/a 1792 8
6006.2.hk \(\chi_{6006}(521, \cdot)\) n/a 3072 8
6006.2.hl \(\chi_{6006}(233, \cdot)\) n/a 3584 8
6006.2.hm \(\chi_{6006}(283, \cdot)\) n/a 1792 8
6006.2.hn \(\chi_{6006}(185, \cdot)\) n/a 3584 8
6006.2.hw \(\chi_{6006}(1219, \cdot)\) n/a 1344 8
6006.2.hx \(\chi_{6006}(29, \cdot)\) n/a 2688 8
6006.2.hy \(\chi_{6006}(139, \cdot)\) n/a 1792 8
6006.2.hz \(\chi_{6006}(251, \cdot)\) n/a 3584 8
6006.2.ia \(\chi_{6006}(457, \cdot)\) n/a 3584 16
6006.2.ib \(\chi_{6006}(691, \cdot)\) n/a 3584 16
6006.2.ic \(\chi_{6006}(137, \cdot)\) n/a 7168 16
6006.2.id \(\chi_{6006}(227, \cdot)\) n/a 7168 16
6006.2.iq \(\chi_{6006}(437, \cdot)\) n/a 7168 16
6006.2.ir \(\chi_{6006}(977, \cdot)\) n/a 7168 16
6006.2.is \(\chi_{6006}(215, \cdot)\) n/a 7168 16
6006.2.it \(\chi_{6006}(317, \cdot)\) n/a 7168 16
6006.2.iu \(\chi_{6006}(71, \cdot)\) n/a 5376 16
6006.2.iv \(\chi_{6006}(41, \cdot)\) n/a 7168 16
6006.2.iw \(\chi_{6006}(31, \cdot)\) n/a 3584 16
6006.2.ix \(\chi_{6006}(193, \cdot)\) n/a 3584 16
6006.2.iy \(\chi_{6006}(115, \cdot)\) n/a 3584 16
6006.2.iz \(\chi_{6006}(151, \cdot)\) n/a 3584 16
6006.2.ja \(\chi_{6006}(85, \cdot)\) n/a 2688 16
6006.2.jb \(\chi_{6006}(97, \cdot)\) n/a 3584 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2002))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3003))\)\(^{\oplus 2}\)