Properties

Label 6630.2
Level 6630
Weight 2
Dimension 261127
Nonzero newspaces 136
Sturm bound 4644864

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Defining parameters

Level: \( N \) = \( 6630 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 136 \)
Sturm bound: \(4644864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6630))\).

Total New Old
Modular forms 1173504 261127 912377
Cusp forms 1148929 261127 887802
Eisenstein series 24575 0 24575

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6630))\)

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
6630.2.a \(\chi_{6630}(1, \cdot)\) 6630.2.a.a 1 1
6630.2.a.b 1
6630.2.a.c 1
6630.2.a.d 1
6630.2.a.e 1
6630.2.a.f 1
6630.2.a.g 1
6630.2.a.h 1
6630.2.a.i 1
6630.2.a.j 1
6630.2.a.k 1
6630.2.a.l 1
6630.2.a.m 1
6630.2.a.n 1
6630.2.a.o 1
6630.2.a.p 1
6630.2.a.q 1
6630.2.a.r 1
6630.2.a.s 1
6630.2.a.t 1
6630.2.a.u 1
6630.2.a.v 1
6630.2.a.w 1
6630.2.a.x 1
6630.2.a.y 1
6630.2.a.z 1
6630.2.a.ba 1
6630.2.a.bb 2
6630.2.a.bc 2
6630.2.a.bd 2
6630.2.a.be 2
6630.2.a.bf 2
6630.2.a.bg 2
6630.2.a.bh 3
6630.2.a.bi 3
6630.2.a.bj 3
6630.2.a.bk 3
6630.2.a.bl 3
6630.2.a.bm 3
6630.2.a.bn 3
6630.2.a.bo 3
6630.2.a.bp 4
6630.2.a.bq 4
6630.2.a.br 4
6630.2.a.bs 4
6630.2.a.bt 4
6630.2.a.bu 4
6630.2.a.bv 4
6630.2.a.bw 5
6630.2.a.bx 5
6630.2.a.by 5
6630.2.a.bz 5
6630.2.a.ca 5
6630.2.a.cb 5
6630.2.a.cc 6
6630.2.c \(\chi_{6630}(4081, \cdot)\) n/a 144 1
6630.2.d \(\chi_{6630}(781, \cdot)\) n/a 144 1
6630.2.g \(\chi_{6630}(2209, \cdot)\) n/a 248 1
6630.2.h \(\chi_{6630}(3979, \cdot)\) n/a 192 1
6630.2.j \(\chi_{6630}(1429, \cdot)\) n/a 224 1
6630.2.m \(\chi_{6630}(4759, \cdot)\) n/a 216 1
6630.2.n \(\chi_{6630}(4861, \cdot)\) n/a 168 1
6630.2.q \(\chi_{6630}(2551, \cdot)\) n/a 304 2
6630.2.s \(\chi_{6630}(2189, \cdot)\) n/a 1008 2
6630.2.u \(\chi_{6630}(3353, \cdot)\) n/a 1008 2
6630.2.w \(\chi_{6630}(1633, \cdot)\) n/a 448 2
6630.2.x \(\chi_{6630}(1087, \cdot)\) n/a 504 2
6630.2.z \(\chi_{6630}(2393, \cdot)\) n/a 864 2
6630.2.bb \(\chi_{6630}(1721, \cdot)\) n/a 672 2
6630.2.be \(\chi_{6630}(443, \cdot)\) n/a 768 2
6630.2.bf \(\chi_{6630}(3583, \cdot)\) n/a 504 2
6630.2.bh \(\chi_{6630}(2257, \cdot)\) n/a 504 2
6630.2.bk \(\chi_{6630}(3977, \cdot)\) n/a 1008 2
6630.2.bm \(\chi_{6630}(1951, \cdot)\) n/a 288 2
6630.2.bn \(\chi_{6630}(2809, \cdot)\) n/a 432 2
6630.2.bq \(\chi_{6630}(239, \cdot)\) n/a 896 2
6630.2.br \(\chi_{6630}(3671, \cdot)\) n/a 672 2
6630.2.bt \(\chi_{6630}(2891, \cdot)\) n/a 608 2
6630.2.bw \(\chi_{6630}(1019, \cdot)\) n/a 1008 2
6630.2.bx \(\chi_{6630}(2911, \cdot)\) n/a 336 2
6630.2.ca \(\chi_{6630}(259, \cdot)\) n/a 496 2
6630.2.cb \(\chi_{6630}(1223, \cdot)\) n/a 864 2
6630.2.ce \(\chi_{6630}(3073, \cdot)\) n/a 504 2
6630.2.cg \(\chi_{6630}(463, \cdot)\) n/a 504 2
6630.2.ch \(\chi_{6630}(3197, \cdot)\) n/a 896 2
6630.2.ck \(\chi_{6630}(2231, \cdot)\) n/a 672 2
6630.2.cl \(\chi_{6630}(2027, \cdot)\) n/a 1008 2
6630.2.co \(\chi_{6630}(307, \cdot)\) n/a 448 2
6630.2.cp \(\chi_{6630}(577, \cdot)\) n/a 504 2
6630.2.cs \(\chi_{6630}(1067, \cdot)\) n/a 864 2
6630.2.ct \(\chi_{6630}(2699, \cdot)\) n/a 1008 2
6630.2.cx \(\chi_{6630}(1291, \cdot)\) n/a 336 2
6630.2.cy \(\chi_{6630}(679, \cdot)\) n/a 512 2
6630.2.db \(\chi_{6630}(4489, \cdot)\) n/a 448 2
6630.2.dd \(\chi_{6630}(919, \cdot)\) n/a 448 2
6630.2.de \(\chi_{6630}(5269, \cdot)\) n/a 496 2
6630.2.dh \(\chi_{6630}(3331, \cdot)\) n/a 336 2
6630.2.di \(\chi_{6630}(511, \cdot)\) n/a 304 2
6630.2.dk \(\chi_{6630}(733, \cdot)\) n/a 1008 4
6630.2.do \(\chi_{6630}(359, \cdot)\) n/a 2016 4
6630.2.dp \(\chi_{6630}(161, \cdot)\) n/a 1344 4
6630.2.dr \(\chi_{6630}(967, \cdot)\) n/a 1008 4
6630.2.ds \(\chi_{6630}(287, \cdot)\) n/a 1728 4
6630.2.dt \(\chi_{6630}(1403, \cdot)\) n/a 2016 4
6630.2.dy \(\chi_{6630}(1171, \cdot)\) n/a 576 4
6630.2.dz \(\chi_{6630}(1039, \cdot)\) n/a 1024 4
6630.2.ea \(\chi_{6630}(859, \cdot)\) n/a 864 4
6630.2.eb \(\chi_{6630}(961, \cdot)\) n/a 672 4
6630.2.eg \(\chi_{6630}(77, \cdot)\) n/a 2016 4
6630.2.eh \(\chi_{6630}(53, \cdot)\) n/a 1728 4
6630.2.ej \(\chi_{6630}(1243, \cdot)\) n/a 1008 4
6630.2.ek \(\chi_{6630}(281, \cdot)\) n/a 1344 4
6630.2.el \(\chi_{6630}(1409, \cdot)\) n/a 2016 4
6630.2.eo \(\chi_{6630}(1477, \cdot)\) n/a 1008 4
6630.2.eq \(\chi_{6630}(3209, \cdot)\) n/a 2016 4
6630.2.es \(\chi_{6630}(1823, \cdot)\) n/a 2016 4
6630.2.ev \(\chi_{6630}(67, \cdot)\) n/a 1008 4
6630.2.ew \(\chi_{6630}(613, \cdot)\) n/a 896 4
6630.2.ez \(\chi_{6630}(2903, \cdot)\) n/a 2016 4
6630.2.fb \(\chi_{6630}(2741, \cdot)\) n/a 1344 4
6630.2.fc \(\chi_{6630}(647, \cdot)\) n/a 1792 4
6630.2.ff \(\chi_{6630}(973, \cdot)\) n/a 1008 4
6630.2.fh \(\chi_{6630}(1033, \cdot)\) n/a 1008 4
6630.2.fi \(\chi_{6630}(2447, \cdot)\) n/a 2016 4
6630.2.fl \(\chi_{6630}(829, \cdot)\) n/a 992 4
6630.2.fm \(\chi_{6630}(361, \cdot)\) n/a 672 4
6630.2.fp \(\chi_{6630}(509, \cdot)\) n/a 2016 4
6630.2.fq \(\chi_{6630}(851, \cdot)\) n/a 1184 4
6630.2.fs \(\chi_{6630}(1631, \cdot)\) n/a 1344 4
6630.2.fv \(\chi_{6630}(1259, \cdot)\) n/a 1792 4
6630.2.fw \(\chi_{6630}(1849, \cdot)\) n/a 1024 4
6630.2.fz \(\chi_{6630}(1381, \cdot)\) n/a 672 4
6630.2.gb \(\chi_{6630}(407, \cdot)\) n/a 2016 4
6630.2.gc \(\chi_{6630}(2767, \cdot)\) n/a 1008 4
6630.2.ge \(\chi_{6630}(3217, \cdot)\) n/a 1008 4
6630.2.gh \(\chi_{6630}(1667, \cdot)\) n/a 1792 4
6630.2.gi \(\chi_{6630}(761, \cdot)\) n/a 1344 4
6630.2.gl \(\chi_{6630}(497, \cdot)\) n/a 2016 4
6630.2.gn \(\chi_{6630}(1393, \cdot)\) n/a 1008 4
6630.2.go \(\chi_{6630}(2143, \cdot)\) n/a 896 4
6630.2.gq \(\chi_{6630}(803, \cdot)\) n/a 2016 4
6630.2.gt \(\chi_{6630}(89, \cdot)\) n/a 2016 4
6630.2.gv \(\chi_{6630}(109, \cdot)\) n/a 2016 8
6630.2.gw \(\chi_{6630}(1507, \cdot)\) n/a 2016 8
6630.2.gx \(\chi_{6630}(313, \cdot)\) n/a 1728 8
6630.2.hb \(\chi_{6630}(31, \cdot)\) n/a 1344 8
6630.2.hc \(\chi_{6630}(317, \cdot)\) n/a 4032 8
6630.2.hg \(\chi_{6630}(779, \cdot)\) n/a 4032 8
6630.2.hh \(\chi_{6630}(131, \cdot)\) n/a 2304 8
6630.2.hi \(\chi_{6630}(2153, \cdot)\) n/a 4032 8
6630.2.hk \(\chi_{6630}(437, \cdot)\) n/a 4032 8
6630.2.ho \(\chi_{6630}(209, \cdot)\) n/a 3456 8
6630.2.hp \(\chi_{6630}(311, \cdot)\) n/a 2688 8
6630.2.hq \(\chi_{6630}(473, \cdot)\) n/a 4032 8
6630.2.ht \(\chi_{6630}(541, \cdot)\) n/a 1344 8
6630.2.hu \(\chi_{6630}(1093, \cdot)\) n/a 1728 8
6630.2.hv \(\chi_{6630}(337, \cdot)\) n/a 2016 8
6630.2.hz \(\chi_{6630}(619, \cdot)\) n/a 2016 8
6630.2.ia \(\chi_{6630}(427, \cdot)\) n/a 2016 8
6630.2.ie \(\chi_{6630}(461, \cdot)\) n/a 2688 8
6630.2.if \(\chi_{6630}(59, \cdot)\) n/a 4032 8
6630.2.ih \(\chi_{6630}(1267, \cdot)\) n/a 2016 8
6630.2.ik \(\chi_{6630}(563, \cdot)\) n/a 4032 8
6630.2.il \(\chi_{6630}(2603, \cdot)\) n/a 4032 8
6630.2.im \(\chi_{6630}(49, \cdot)\) n/a 2048 8
6630.2.in \(\chi_{6630}(451, \cdot)\) n/a 1344 8
6630.2.is \(\chi_{6630}(121, \cdot)\) n/a 1344 8
6630.2.it \(\chi_{6630}(529, \cdot)\) n/a 1984 8
6630.2.iu \(\chi_{6630}(263, \cdot)\) n/a 4032 8
6630.2.iv \(\chi_{6630}(257, \cdot)\) n/a 4032 8
6630.2.iz \(\chi_{6630}(457, \cdot)\) n/a 2016 8
6630.2.ja \(\chi_{6630}(869, \cdot)\) n/a 4032 8
6630.2.jb \(\chi_{6630}(3521, \cdot)\) n/a 2688 8
6630.2.je \(\chi_{6630}(223, \cdot)\) n/a 2016 8
6630.2.jg \(\chi_{6630}(301, \cdot)\) n/a 2688 16
6630.2.jk \(\chi_{6630}(517, \cdot)\) n/a 4032 16
6630.2.jl \(\chi_{6630}(607, \cdot)\) n/a 4032 16
6630.2.jm \(\chi_{6630}(709, \cdot)\) n/a 4032 16
6630.2.jp \(\chi_{6630}(743, \cdot)\) n/a 8064 16
6630.2.jq \(\chi_{6630}(29, \cdot)\) n/a 8064 16
6630.2.jr \(\chi_{6630}(641, \cdot)\) n/a 5376 16
6630.2.jv \(\chi_{6630}(167, \cdot)\) n/a 8064 16
6630.2.jx \(\chi_{6630}(617, \cdot)\) n/a 8064 16
6630.2.jy \(\chi_{6630}(329, \cdot)\) n/a 8064 16
6630.2.jz \(\chi_{6630}(581, \cdot)\) n/a 5376 16
6630.2.kd \(\chi_{6630}(197, \cdot)\) n/a 8064 16
6630.2.ke \(\chi_{6630}(379, \cdot)\) n/a 4032 16
6630.2.ki \(\chi_{6630}(133, \cdot)\) n/a 4032 16
6630.2.kj \(\chi_{6630}(277, \cdot)\) n/a 4032 16
6630.2.kk \(\chi_{6630}(241, \cdot)\) n/a 2688 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6630))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6630)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(442))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1326))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3315))\)\(^{\oplus 2}\)