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Properties

Label 6930.2
Level 6930
Weight 2
Dimension 283616
Nonzero newspaces 120
Sturm bound 4976640

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Defining parameters

Level: \( N \) = \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(4976640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6930))\).

Total New Old
Modular forms 1259520 283616 975904
Cusp forms 1228801 283616 945185
Eisenstein series 30719 0 30719

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6930))\)

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
6930.2.a \(\chi_{6930}(1, \cdot)\) 6930.2.a.a 1 1
6930.2.a.b 1
6930.2.a.c 1
6930.2.a.d 1
6930.2.a.e 1
6930.2.a.f 1
6930.2.a.g 1
6930.2.a.h 1
6930.2.a.i 1
6930.2.a.j 1
6930.2.a.k 1
6930.2.a.l 1
6930.2.a.m 1
6930.2.a.n 1
6930.2.a.o 1
6930.2.a.p 1
6930.2.a.q 1
6930.2.a.r 1
6930.2.a.s 1
6930.2.a.t 1
6930.2.a.u 1
6930.2.a.v 1
6930.2.a.w 1
6930.2.a.x 1
6930.2.a.y 1
6930.2.a.z 1
6930.2.a.ba 1
6930.2.a.bb 1
6930.2.a.bc 1
6930.2.a.bd 1
6930.2.a.be 1
6930.2.a.bf 1
6930.2.a.bg 1
6930.2.a.bh 1
6930.2.a.bi 1
6930.2.a.bj 1
6930.2.a.bk 1
6930.2.a.bl 1
6930.2.a.bm 1
6930.2.a.bn 2
6930.2.a.bo 2
6930.2.a.bp 2
6930.2.a.bq 2
6930.2.a.br 2
6930.2.a.bs 2
6930.2.a.bt 2
6930.2.a.bu 2
6930.2.a.bv 2
6930.2.a.bw 2
6930.2.a.bx 2
6930.2.a.by 2
6930.2.a.bz 2
6930.2.a.ca 2
6930.2.a.cb 2
6930.2.a.cc 2
6930.2.a.cd 2
6930.2.a.ce 3
6930.2.a.cf 3
6930.2.a.cg 3
6930.2.a.ch 3
6930.2.a.ci 3
6930.2.a.cj 3
6930.2.a.ck 3
6930.2.a.cl 3
6930.2.a.cm 3
6930.2.d \(\chi_{6930}(3079, \cdot)\) n/a 240 1
6930.2.e \(\chi_{6930}(4159, \cdot)\) n/a 148 1
6930.2.f \(\chi_{6930}(881, \cdot)\) 6930.2.f.a 24 1
6930.2.f.b 24
6930.2.f.c 24
6930.2.f.d 24
6930.2.g \(\chi_{6930}(5741, \cdot)\) 6930.2.g.a 24 1
6930.2.g.b 24
6930.2.g.c 24
6930.2.g.d 24
6930.2.j \(\chi_{6930}(5039, \cdot)\) n/a 160 1
6930.2.k \(\chi_{6930}(2969, \cdot)\) n/a 144 1
6930.2.p \(\chi_{6930}(5851, \cdot)\) n/a 160 1
6930.2.q \(\chi_{6930}(2641, \cdot)\) n/a 640 2
6930.2.r \(\chi_{6930}(331, \cdot)\) n/a 640 2
6930.2.s \(\chi_{6930}(2311, \cdot)\) n/a 480 2
6930.2.t \(\chi_{6930}(991, \cdot)\) n/a 272 2
6930.2.u \(\chi_{6930}(4157, \cdot)\) n/a 384 2
6930.2.x \(\chi_{6930}(5237, \cdot)\) n/a 240 2
6930.2.y \(\chi_{6930}(5347, \cdot)\) n/a 400 2
6930.2.bb \(\chi_{6930}(3277, \cdot)\) n/a 360 2
6930.2.bc \(\chi_{6930}(631, \cdot)\) n/a 480 4
6930.2.bf \(\chi_{6930}(2861, \cdot)\) n/a 224 2
6930.2.bg \(\chi_{6930}(3761, \cdot)\) n/a 256 2
6930.2.bh \(\chi_{6930}(2089, \cdot)\) n/a 480 2
6930.2.bi \(\chi_{6930}(2179, \cdot)\) n/a 400 2
6930.2.bl \(\chi_{6930}(659, \cdot)\) n/a 864 2
6930.2.bm \(\chi_{6930}(419, \cdot)\) n/a 960 2
6930.2.bp \(\chi_{6930}(241, \cdot)\) n/a 768 2
6930.2.bq \(\chi_{6930}(2551, \cdot)\) n/a 768 2
6930.2.bz \(\chi_{6930}(1649, \cdot)\) n/a 1152 2
6930.2.ca \(\chi_{6930}(1739, \cdot)\) n/a 960 2
6930.2.cb \(\chi_{6930}(5609, \cdot)\) n/a 1152 2
6930.2.cc \(\chi_{6930}(4709, \cdot)\) n/a 960 2
6930.2.cf \(\chi_{6930}(1231, \cdot)\) n/a 768 2
6930.2.ci \(\chi_{6930}(1849, \cdot)\) n/a 720 2
6930.2.cj \(\chi_{6930}(769, \cdot)\) n/a 1152 2
6930.2.co \(\chi_{6930}(1451, \cdot)\) n/a 768 2
6930.2.cp \(\chi_{6930}(551, \cdot)\) n/a 640 2
6930.2.cq \(\chi_{6930}(4421, \cdot)\) n/a 768 2
6930.2.cr \(\chi_{6930}(4511, \cdot)\) n/a 640 2
6930.2.cs \(\chi_{6930}(2839, \cdot)\) n/a 960 2
6930.2.ct \(\chi_{6930}(439, \cdot)\) n/a 1152 2
6930.2.cu \(\chi_{6930}(529, \cdot)\) n/a 960 2
6930.2.cv \(\chi_{6930}(2749, \cdot)\) n/a 1152 2
6930.2.da \(\chi_{6930}(1121, \cdot)\) n/a 576 2
6930.2.db \(\chi_{6930}(3191, \cdot)\) n/a 640 2
6930.2.de \(\chi_{6930}(901, \cdot)\) n/a 320 2
6930.2.dj \(\chi_{6930}(89, \cdot)\) n/a 320 2
6930.2.dk \(\chi_{6930}(989, \cdot)\) n/a 384 2
6930.2.dl \(\chi_{6930}(811, \cdot)\) n/a 640 4
6930.2.dq \(\chi_{6930}(2339, \cdot)\) n/a 576 4
6930.2.dr \(\chi_{6930}(1259, \cdot)\) n/a 768 4
6930.2.du \(\chi_{6930}(701, \cdot)\) n/a 384 4
6930.2.dv \(\chi_{6930}(251, \cdot)\) n/a 512 4
6930.2.dw \(\chi_{6930}(379, \cdot)\) n/a 720 4
6930.2.dx \(\chi_{6930}(2449, \cdot)\) n/a 960 4
6930.2.ea \(\chi_{6930}(617, \cdot)\) n/a 1440 4
6930.2.ed \(\chi_{6930}(923, \cdot)\) n/a 2304 4
6930.2.ef \(\chi_{6930}(397, \cdot)\) n/a 800 4
6930.2.eh \(\chi_{6930}(1957, \cdot)\) n/a 2304 4
6930.2.ej \(\chi_{6930}(373, \cdot)\) n/a 2304 4
6930.2.ek \(\chi_{6930}(1123, \cdot)\) n/a 1920 4
6930.2.em \(\chi_{6930}(2047, \cdot)\) n/a 1920 4
6930.2.eo \(\chi_{6930}(1297, \cdot)\) n/a 960 4
6930.2.er \(\chi_{6930}(593, \cdot)\) n/a 768 4
6930.2.et \(\chi_{6930}(947, \cdot)\) n/a 1920 4
6930.2.ev \(\chi_{6930}(23, \cdot)\) n/a 1920 4
6930.2.ew \(\chi_{6930}(857, \cdot)\) n/a 2304 4
6930.2.ey \(\chi_{6930}(3827, \cdot)\) n/a 2304 4
6930.2.fa \(\chi_{6930}(683, \cdot)\) n/a 640 4
6930.2.fc \(\chi_{6930}(43, \cdot)\) n/a 1728 4
6930.2.ff \(\chi_{6930}(727, \cdot)\) n/a 1920 4
6930.2.fg \(\chi_{6930}(361, \cdot)\) n/a 1280 8
6930.2.fh \(\chi_{6930}(421, \cdot)\) n/a 2304 8
6930.2.fi \(\chi_{6930}(751, \cdot)\) n/a 3072 8
6930.2.fj \(\chi_{6930}(961, \cdot)\) n/a 3072 8
6930.2.fk \(\chi_{6930}(127, \cdot)\) n/a 1440 8
6930.2.fn \(\chi_{6930}(433, \cdot)\) n/a 1920 8
6930.2.fo \(\chi_{6930}(323, \cdot)\) n/a 1152 8
6930.2.fr \(\chi_{6930}(503, \cdot)\) n/a 1536 8
6930.2.fs \(\chi_{6930}(359, \cdot)\) n/a 1536 8
6930.2.ft \(\chi_{6930}(269, \cdot)\) n/a 1536 8
6930.2.fy \(\chi_{6930}(271, \cdot)\) n/a 1280 8
6930.2.gb \(\chi_{6930}(1301, \cdot)\) n/a 3072 8
6930.2.gc \(\chi_{6930}(281, \cdot)\) n/a 2304 8
6930.2.gh \(\chi_{6930}(409, \cdot)\) n/a 4608 8
6930.2.gi \(\chi_{6930}(709, \cdot)\) n/a 4608 8
6930.2.gj \(\chi_{6930}(1249, \cdot)\) n/a 4608 8
6930.2.gk \(\chi_{6930}(499, \cdot)\) n/a 4608 8
6930.2.gl \(\chi_{6930}(311, \cdot)\) n/a 3072 8
6930.2.gm \(\chi_{6930}(821, \cdot)\) n/a 3072 8
6930.2.gn \(\chi_{6930}(731, \cdot)\) n/a 3072 8
6930.2.go \(\chi_{6930}(1031, \cdot)\) n/a 3072 8
6930.2.gt \(\chi_{6930}(139, \cdot)\) n/a 4608 8
6930.2.gu \(\chi_{6930}(169, \cdot)\) n/a 3456 8
6930.2.gx \(\chi_{6930}(391, \cdot)\) n/a 3072 8
6930.2.ha \(\chi_{6930}(509, \cdot)\) n/a 4608 8
6930.2.hb \(\chi_{6930}(149, \cdot)\) n/a 4608 8
6930.2.hc \(\chi_{6930}(59, \cdot)\) n/a 4608 8
6930.2.hd \(\chi_{6930}(569, \cdot)\) n/a 4608 8
6930.2.hm \(\chi_{6930}(481, \cdot)\) n/a 3072 8
6930.2.hn \(\chi_{6930}(61, \cdot)\) n/a 3072 8
6930.2.hq \(\chi_{6930}(839, \cdot)\) n/a 4608 8
6930.2.hr \(\chi_{6930}(29, \cdot)\) n/a 3456 8
6930.2.hu \(\chi_{6930}(289, \cdot)\) n/a 1920 8
6930.2.hv \(\chi_{6930}(19, \cdot)\) n/a 1920 8
6930.2.hw \(\chi_{6930}(431, \cdot)\) n/a 1024 8
6930.2.hx \(\chi_{6930}(521, \cdot)\) n/a 1024 8
6930.2.ia \(\chi_{6930}(97, \cdot)\) n/a 9216 16
6930.2.id \(\chi_{6930}(337, \cdot)\) n/a 6912 16
6930.2.if \(\chi_{6930}(53, \cdot)\) n/a 3072 16
6930.2.ih \(\chi_{6930}(173, \cdot)\) n/a 9216 16
6930.2.ij \(\chi_{6930}(227, \cdot)\) n/a 9216 16
6930.2.ik \(\chi_{6930}(137, \cdot)\) n/a 9216 16
6930.2.im \(\chi_{6930}(317, \cdot)\) n/a 9216 16
6930.2.io \(\chi_{6930}(17, \cdot)\) n/a 3072 16
6930.2.ir \(\chi_{6930}(613, \cdot)\) n/a 3840 16
6930.2.it \(\chi_{6930}(157, \cdot)\) n/a 9216 16
6930.2.iv \(\chi_{6930}(103, \cdot)\) n/a 9216 16
6930.2.iw \(\chi_{6930}(277, \cdot)\) n/a 9216 16
6930.2.iy \(\chi_{6930}(193, \cdot)\) n/a 9216 16
6930.2.ja \(\chi_{6930}(577, \cdot)\) n/a 3840 16
6930.2.jc \(\chi_{6930}(83, \cdot)\) n/a 9216 16
6930.2.jf \(\chi_{6930}(113, \cdot)\) n/a 6912 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6930))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3465))\)\(^{\oplus 2}\)