# Properties

 Label 7105.2 Level 7105 Weight 2 Dimension 1725892 Nonzero newspaces 180 Sturm bound 7902720

## Defining parameters

 Level: $$N$$ = $$7105 = 5 \cdot 7^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$180$$ Sturm bound: $$7902720$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7105))$$.

Total New Old
Modular forms 1989120 1741608 247512
Cusp forms 1962241 1725892 236349
Eisenstein series 26879 15716 11163

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7105))$$

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
7105.2.a $$\chi_{7105}(1, \cdot)$$ 7105.2.a.a 1 1
7105.2.a.b 1
7105.2.a.c 1
7105.2.a.d 1
7105.2.a.e 2
7105.2.a.f 2
7105.2.a.g 2
7105.2.a.h 2
7105.2.a.i 2
7105.2.a.j 2
7105.2.a.k 2
7105.2.a.l 3
7105.2.a.m 3
7105.2.a.n 3
7105.2.a.o 3
7105.2.a.p 3
7105.2.a.q 6
7105.2.a.r 7
7105.2.a.s 7
7105.2.a.t 8
7105.2.a.u 11
7105.2.a.v 14
7105.2.a.w 14
7105.2.a.x 14
7105.2.a.y 14
7105.2.a.z 17
7105.2.a.ba 17
7105.2.a.bb 17
7105.2.a.bc 17
7105.2.a.bd 19
7105.2.a.be 19
7105.2.a.bf 21
7105.2.a.bg 21
7105.2.a.bh 26
7105.2.a.bi 26
7105.2.a.bj 28
7105.2.a.bk 28
7105.2.b $$\chi_{7105}(2696, \cdot)$$ n/a 410 1
7105.2.c $$\chi_{7105}(4264, \cdot)$$ n/a 574 1
7105.2.h $$\chi_{7105}(6959, \cdot)$$ n/a 604 1
7105.2.i $$\chi_{7105}(1451, \cdot)$$ n/a 744 2
7105.2.k $$\chi_{7105}(2598, \cdot)$$ n/a 1210 2
7105.2.l $$\chi_{7105}(4262, \cdot)$$ n/a 1184 2
7105.2.o $$\chi_{7105}(1567, \cdot)$$ n/a 1120 2
7105.2.q $$\chi_{7105}(244, \cdot)$$ n/a 1184 2
7105.2.r $$\chi_{7105}(3086, \cdot)$$ n/a 800 2
7105.2.t $$\chi_{7105}(1177, \cdot)$$ n/a 1210 2
7105.2.v $$\chi_{7105}(1304, \cdot)$$ n/a 1184 2
7105.2.ba $$\chi_{7105}(5714, \cdot)$$ n/a 1120 2
7105.2.bb $$\chi_{7105}(4146, \cdot)$$ n/a 800 2
7105.2.bc $$\chi_{7105}(1611, \cdot)$$ n/a 3360 6
7105.2.bd $$\chi_{7105}(281, \cdot)$$ n/a 3360 6
7105.2.be $$\chi_{7105}(36, \cdot)$$ n/a 3360 6
7105.2.bf $$\chi_{7105}(1016, \cdot)$$ n/a 3120 6
7105.2.bg $$\chi_{7105}(981, \cdot)$$ n/a 2460 6
7105.2.bh $$\chi_{7105}(596, \cdot)$$ n/a 3360 6
7105.2.bi $$\chi_{7105}(141, \cdot)$$ n/a 3360 6
7105.2.bj $$\chi_{7105}(1821, \cdot)$$ n/a 3360 6
7105.2.bl $$\chi_{7105}(128, \cdot)$$ n/a 2368 4
7105.2.bm $$\chi_{7105}(117, \cdot)$$ n/a 2240 4
7105.2.bp $$\chi_{7105}(1942, \cdot)$$ n/a 2368 4
7105.2.br $$\chi_{7105}(1844, \cdot)$$ n/a 2368 4
7105.2.bs $$\chi_{7105}(766, \cdot)$$ n/a 1600 4
7105.2.bu $$\chi_{7105}(4048, \cdot)$$ n/a 2368 4
7105.2.by $$\chi_{7105}(1359, \cdot)$$ n/a 5016 6
7105.2.bz $$\chi_{7105}(71, \cdot)$$ n/a 3360 6
7105.2.cc $$\chi_{7105}(274, \cdot)$$ n/a 5016 6
7105.2.cd $$\chi_{7105}(1289, \cdot)$$ n/a 5016 6
7105.2.ce $$\chi_{7105}(64, \cdot)$$ n/a 5016 6
7105.2.cf $$\chi_{7105}(869, \cdot)$$ n/a 5016 6
7105.2.cg $$\chi_{7105}(589, \cdot)$$ n/a 3624 6
7105.2.ch $$\chi_{7105}(1744, \cdot)$$ n/a 5016 6
7105.2.cu $$\chi_{7105}(729, \cdot)$$ n/a 5016 6
7105.2.cv $$\chi_{7105}(1891, \cdot)$$ n/a 3360 6
7105.2.cw $$\chi_{7105}(169, \cdot)$$ n/a 5016 6
7105.2.dj $$\chi_{7105}(344, \cdot)$$ n/a 3636 6
7105.2.dk $$\chi_{7105}(204, \cdot)$$ n/a 4704 6
7105.2.dl $$\chi_{7105}(1184, \cdot)$$ n/a 5016 6
7105.2.dm $$\chi_{7105}(239, \cdot)$$ n/a 5016 6
7105.2.dn $$\chi_{7105}(1254, \cdot)$$ n/a 5016 6
7105.2.do $$\chi_{7105}(1716, \cdot)$$ n/a 2460 6
7105.2.dp $$\chi_{7105}(666, \cdot)$$ n/a 3360 6
7105.2.dq $$\chi_{7105}(1541, \cdot)$$ n/a 3360 6
7105.2.dr $$\chi_{7105}(631, \cdot)$$ n/a 3360 6
7105.2.ds $$\chi_{7105}(876, \cdot)$$ n/a 3360 6
7105.2.dt $$\chi_{7105}(484, \cdot)$$ n/a 5016 6
7105.2.du $$\chi_{7105}(386, \cdot)$$ n/a 3360 6
7105.2.dx $$\chi_{7105}(2934, \cdot)$$ n/a 5016 6
7105.2.ea $$\chi_{7105}(571, \cdot)$$ n/a 6720 12
7105.2.eb $$\chi_{7105}(81, \cdot)$$ n/a 6720 12
7105.2.ec $$\chi_{7105}(226, \cdot)$$ n/a 4800 12
7105.2.ed $$\chi_{7105}(291, \cdot)$$ n/a 6288 12
7105.2.ee $$\chi_{7105}(1486, \cdot)$$ n/a 6720 12
7105.2.ef $$\chi_{7105}(16, \cdot)$$ n/a 6720 12
7105.2.eg $$\chi_{7105}(1241, \cdot)$$ n/a 6720 12
7105.2.eh $$\chi_{7105}(401, \cdot)$$ n/a 6720 12
7105.2.ei $$\chi_{7105}(617, \cdot)$$ n/a 10032 12
7105.2.ek $$\chi_{7105}(1772, \cdot)$$ n/a 10032 12
7105.2.er $$\chi_{7105}(743, \cdot)$$ n/a 10032 12
7105.2.es $$\chi_{7105}(1128, \cdot)$$ n/a 7260 12
7105.2.et $$\chi_{7105}(127, \cdot)$$ n/a 10032 12
7105.2.eu $$\chi_{7105}(8, \cdot)$$ n/a 10032 12
7105.2.ev $$\chi_{7105}(218, \cdot)$$ n/a 10032 12
7105.2.ew $$\chi_{7105}(162, \cdot)$$ n/a 10032 12
7105.2.ez $$\chi_{7105}(76, \cdot)$$ n/a 6720 12
7105.2.fa $$\chi_{7105}(454, \cdot)$$ n/a 10032 12
7105.2.fc $$\chi_{7105}(1602, \cdot)$$ n/a 10032 12
7105.2.ff $$\chi_{7105}(62, \cdot)$$ n/a 10032 12
7105.2.fg $$\chi_{7105}(748, \cdot)$$ n/a 10032 12
7105.2.fj $$\chi_{7105}(937, \cdot)$$ n/a 10032 12
7105.2.fl $$\chi_{7105}(1784, \cdot)$$ n/a 10032 12
7105.2.fm $$\chi_{7105}(251, \cdot)$$ n/a 6720 12
7105.2.ft $$\chi_{7105}(2911, \cdot)$$ n/a 6720 12
7105.2.fu $$\chi_{7105}(461, \cdot)$$ n/a 6720 12
7105.2.fv $$\chi_{7105}(391, \cdot)$$ n/a 4800 12
7105.2.fw $$\chi_{7105}(41, \cdot)$$ n/a 6720 12
7105.2.fx $$\chi_{7105}(356, \cdot)$$ n/a 6720 12
7105.2.fy $$\chi_{7105}(279, \cdot)$$ n/a 10032 12
7105.2.fz $$\chi_{7105}(104, \cdot)$$ n/a 10032 12
7105.2.ga $$\chi_{7105}(1469, \cdot)$$ n/a 7104 12
7105.2.gb $$\chi_{7105}(769, \cdot)$$ n/a 10032 12
7105.2.gc $$\chi_{7105}(69, \cdot)$$ n/a 10032 12
7105.2.gi $$\chi_{7105}(13, \cdot)$$ n/a 10032 12
7105.2.gl $$\chi_{7105}(517, \cdot)$$ n/a 10032 12
7105.2.gm $$\chi_{7105}(342, \cdot)$$ n/a 7104 12
7105.2.gn $$\chi_{7105}(1357, \cdot)$$ n/a 10032 12
7105.2.go $$\chi_{7105}(132, \cdot)$$ n/a 10032 12
7105.2.gp $$\chi_{7105}(83, \cdot)$$ n/a 10032 12
7105.2.gq $$\chi_{7105}(552, \cdot)$$ n/a 9408 12
7105.2.hb $$\chi_{7105}(202, \cdot)$$ n/a 10032 12
7105.2.hc $$\chi_{7105}(622, \cdot)$$ n/a 10032 12
7105.2.hd $$\chi_{7105}(167, \cdot)$$ n/a 10032 12
7105.2.he $$\chi_{7105}(1028, \cdot)$$ n/a 7104 12
7105.2.hf $$\chi_{7105}(237, \cdot)$$ n/a 10032 12
7105.2.hh $$\chi_{7105}(706, \cdot)$$ n/a 6720 12
7105.2.hi $$\chi_{7105}(524, \cdot)$$ n/a 10032 12
7105.2.hl $$\chi_{7105}(897, \cdot)$$ n/a 10032 12
7105.2.hm $$\chi_{7105}(302, \cdot)$$ n/a 10032 12
7105.2.hn $$\chi_{7105}(43, \cdot)$$ n/a 10032 12
7105.2.ho $$\chi_{7105}(2367, \cdot)$$ n/a 10032 12
7105.2.hp $$\chi_{7105}(253, \cdot)$$ n/a 10032 12
7105.2.hq $$\chi_{7105}(148, \cdot)$$ n/a 7260 12
7105.2.hx $$\chi_{7105}(1058, \cdot)$$ n/a 10032 12
7105.2.hz $$\chi_{7105}(113, \cdot)$$ n/a 10032 12
7105.2.ic $$\chi_{7105}(149, \cdot)$$ n/a 10032 12
7105.2.if $$\chi_{7105}(151, \cdot)$$ n/a 6720 12
7105.2.ig $$\chi_{7105}(506, \cdot)$$ n/a 6720 12
7105.2.ih $$\chi_{7105}(51, \cdot)$$ n/a 6720 12
7105.2.ii $$\chi_{7105}(86, \cdot)$$ n/a 6720 12
7105.2.ij $$\chi_{7105}(361, \cdot)$$ n/a 4800 12
7105.2.ik $$\chi_{7105}(284, \cdot)$$ n/a 10032 12
7105.2.il $$\chi_{7105}(674, \cdot)$$ n/a 10032 12
7105.2.im $$\chi_{7105}(74, \cdot)$$ n/a 10032 12
7105.2.in $$\chi_{7105}(494, \cdot)$$ n/a 9408 12
7105.2.io $$\chi_{7105}(459, \cdot)$$ n/a 7104 12
7105.2.ip $$\chi_{7105}(296, \cdot)$$ n/a 6720 12
7105.2.iq $$\chi_{7105}(774, \cdot)$$ n/a 10032 12
7105.2.jd $$\chi_{7105}(429, \cdot)$$ n/a 10032 12
7105.2.je $$\chi_{7105}(121, \cdot)$$ n/a 6720 12
7105.2.jf $$\chi_{7105}(9, \cdot)$$ n/a 10032 12
7105.2.js $$\chi_{7105}(324, \cdot)$$ n/a 7104 12
7105.2.jt $$\chi_{7105}(144, \cdot)$$ n/a 10032 12
7105.2.ju $$\chi_{7105}(109, \cdot)$$ n/a 10032 12
7105.2.jv $$\chi_{7105}(4, \cdot)$$ n/a 10032 12
7105.2.jw $$\chi_{7105}(179, \cdot)$$ n/a 10032 12
7105.2.jx $$\chi_{7105}(354, \cdot)$$ n/a 10032 12
7105.2.ka $$\chi_{7105}(821, \cdot)$$ n/a 6720 12
7105.2.kb $$\chi_{7105}(219, \cdot)$$ n/a 10032 12
7105.2.ke $$\chi_{7105}(282, \cdot)$$ n/a 20064 24
7105.2.kg $$\chi_{7105}(142, \cdot)$$ n/a 20064 24
7105.2.kn $$\chi_{7105}(172, \cdot)$$ n/a 20064 24
7105.2.ko $$\chi_{7105}(263, \cdot)$$ n/a 14208 24
7105.2.kp $$\chi_{7105}(627, \cdot)$$ n/a 20064 24
7105.2.kq $$\chi_{7105}(102, \cdot)$$ n/a 20064 24
7105.2.kr $$\chi_{7105}(333, \cdot)$$ n/a 20064 24
7105.2.ks $$\chi_{7105}(592, \cdot)$$ n/a 20064 24
7105.2.ku $$\chi_{7105}(528, \cdot)$$ n/a 20064 24
7105.2.kx $$\chi_{7105}(103, \cdot)$$ n/a 20064 24
7105.2.ld $$\chi_{7105}(131, \cdot)$$ n/a 13440 24
7105.2.le $$\chi_{7105}(206, \cdot)$$ n/a 13440 24
7105.2.lf $$\chi_{7105}(31, \cdot)$$ n/a 9600 24
7105.2.lg $$\chi_{7105}(481, \cdot)$$ n/a 13440 24
7105.2.lh $$\chi_{7105}(61, \cdot)$$ n/a 13440 24
7105.2.li $$\chi_{7105}(234, \cdot)$$ n/a 20064 24
7105.2.lj $$\chi_{7105}(684, \cdot)$$ n/a 20064 24
7105.2.lk $$\chi_{7105}(19, \cdot)$$ n/a 14208 24
7105.2.ll $$\chi_{7105}(229, \cdot)$$ n/a 20064 24
7105.2.lm $$\chi_{7105}(124, \cdot)$$ n/a 20064 24
7105.2.lt $$\chi_{7105}(159, \cdot)$$ n/a 20064 24
7105.2.lu $$\chi_{7105}(1291, \cdot)$$ n/a 13440 24
7105.2.lw $$\chi_{7105}(283, \cdot)$$ n/a 20064 24
7105.2.lx $$\chi_{7105}(122, \cdot)$$ n/a 20064 24
7105.2.ly $$\chi_{7105}(38, \cdot)$$ n/a 20064 24
7105.2.lz $$\chi_{7105}(178, \cdot)$$ n/a 14208 24
7105.2.ma $$\chi_{7105}(173, \cdot)$$ n/a 20064 24
7105.2.ml $$\chi_{7105}(262, \cdot)$$ n/a 18816 24
7105.2.mm $$\chi_{7105}(808, \cdot)$$ n/a 20064 24
7105.2.mn $$\chi_{7105}(227, \cdot)$$ n/a 14208 24
7105.2.mo $$\chi_{7105}(857, \cdot)$$ n/a 20064 24
7105.2.mp $$\chi_{7105}(397, \cdot)$$ n/a 20064 24
7105.2.mq $$\chi_{7105}(152, \cdot)$$ n/a 20064 24
7105.2.mt $$\chi_{7105}(33, \cdot)$$ n/a 20064 24
7105.2.mv $$\chi_{7105}(26, \cdot)$$ n/a 13440 24
7105.2.mw $$\chi_{7105}(89, \cdot)$$ n/a 20064 24
7105.2.mz $$\chi_{7105}(66, \cdot)$$ n/a 13440 24
7105.2.na $$\chi_{7105}(549, \cdot)$$ n/a 20064 24
7105.2.nc $$\chi_{7105}(138, \cdot)$$ n/a 20064 24
7105.2.nf $$\chi_{7105}(52, \cdot)$$ n/a 20064 24
7105.2.nh $$\chi_{7105}(137, \cdot)$$ n/a 20064 24
7105.2.ni $$\chi_{7105}(452, \cdot)$$ n/a 20064 24
7105.2.nj $$\chi_{7105}(72, \cdot)$$ n/a 20064 24
7105.2.nk $$\chi_{7105}(2, \cdot)$$ n/a 20064 24
7105.2.nl $$\chi_{7105}(298, \cdot)$$ n/a 20064 24
7105.2.nm $$\chi_{7105}(18, \cdot)$$ n/a 14208 24
7105.2.nt $$\chi_{7105}(947, \cdot)$$ n/a 20064 24
7105.2.nv $$\chi_{7105}(37, \cdot)$$ n/a 20064 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7105))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7105)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(203))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1015))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1421))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7105))$$$$^{\oplus 1}$$