# Properties

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

## 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 the 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

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