Properties

 Label 6160.2 Level 6160 Weight 2 Dimension 534944 Nonzero newspaces 112 Sturm bound 4423680

Defining parameters

 Level: $$N$$ = $$6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$112$$ Sturm bound: $$4423680$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6160))$$.

Total New Old
Modular forms 1119360 539800 579560
Cusp forms 1092481 534944 557537
Eisenstein series 26879 4856 22023

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6160))$$

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
6160.2.a $$\chi_{6160}(1, \cdot)$$ 6160.2.a.a 1 1
6160.2.a.b 1
6160.2.a.c 1
6160.2.a.d 1
6160.2.a.e 1
6160.2.a.f 1
6160.2.a.g 1
6160.2.a.h 1
6160.2.a.i 1
6160.2.a.j 1
6160.2.a.k 1
6160.2.a.l 1
6160.2.a.m 1
6160.2.a.n 1
6160.2.a.o 1
6160.2.a.p 1
6160.2.a.q 1
6160.2.a.r 2
6160.2.a.s 2
6160.2.a.t 2
6160.2.a.u 2
6160.2.a.v 2
6160.2.a.w 2
6160.2.a.x 2
6160.2.a.y 2
6160.2.a.z 2
6160.2.a.ba 2
6160.2.a.bb 2
6160.2.a.bc 2
6160.2.a.bd 3
6160.2.a.be 3
6160.2.a.bf 3
6160.2.a.bg 3
6160.2.a.bh 3
6160.2.a.bi 3
6160.2.a.bj 3
6160.2.a.bk 3
6160.2.a.bl 3
6160.2.a.bm 3
6160.2.a.bn 3
6160.2.a.bo 3
6160.2.a.bp 3
6160.2.a.bq 4
6160.2.a.br 4
6160.2.a.bs 4
6160.2.a.bt 4
6160.2.a.bu 4
6160.2.a.bv 5
6160.2.a.bw 5
6160.2.a.bx 5
6160.2.a.by 5
6160.2.d $$\chi_{6160}(351, \cdot)$$ n/a 144 1
6160.2.e $$\chi_{6160}(4929, \cdot)$$ n/a 180 1
6160.2.f $$\chi_{6160}(3081, \cdot)$$ None 0 1
6160.2.g $$\chi_{6160}(2199, \cdot)$$ None 0 1
6160.2.j $$\chi_{6160}(3191, \cdot)$$ None 0 1
6160.2.k $$\chi_{6160}(3849, \cdot)$$ None 0 1
6160.2.p $$\chi_{6160}(2001, \cdot)$$ n/a 192 1
6160.2.q $$\chi_{6160}(5039, \cdot)$$ n/a 240 1
6160.2.t $$\chi_{6160}(769, \cdot)$$ n/a 284 1
6160.2.u $$\chi_{6160}(111, \cdot)$$ n/a 160 1
6160.2.v $$\chi_{6160}(1959, \cdot)$$ None 0 1
6160.2.w $$\chi_{6160}(5081, \cdot)$$ None 0 1
6160.2.z $$\chi_{6160}(1849, \cdot)$$ None 0 1
6160.2.ba $$\chi_{6160}(3431, \cdot)$$ None 0 1
6160.2.bf $$\chi_{6160}(5279, \cdot)$$ n/a 216 1
6160.2.bg $$\chi_{6160}(1761, \cdot)$$ n/a 320 2
6160.2.bh $$\chi_{6160}(3037, \cdot)$$ n/a 1920 2
6160.2.bj $$\chi_{6160}(3387, \cdot)$$ n/a 2288 2
6160.2.bm $$\chi_{6160}(4467, \cdot)$$ n/a 1440 2
6160.2.bo $$\chi_{6160}(197, \cdot)$$ n/a 1728 2
6160.2.bt $$\chi_{6160}(1891, \cdot)$$ n/a 1152 2
6160.2.bu $$\chi_{6160}(2309, \cdot)$$ n/a 2288 2
6160.2.bv $$\chi_{6160}(309, \cdot)$$ n/a 1440 2
6160.2.bw $$\chi_{6160}(1651, \cdot)$$ n/a 1280 2
6160.2.bx $$\chi_{6160}(1847, \cdot)$$ None 0 2
6160.2.ca $$\chi_{6160}(1737, \cdot)$$ None 0 2
6160.2.cb $$\chi_{6160}(1497, \cdot)$$ None 0 2
6160.2.ce $$\chi_{6160}(3543, \cdot)$$ None 0 2
6160.2.cg $$\chi_{6160}(2113, \cdot)$$ n/a 480 2
6160.2.ch $$\chi_{6160}(463, \cdot)$$ n/a 360 2
6160.2.ck $$\chi_{6160}(2463, \cdot)$$ n/a 576 2
6160.2.cl $$\chi_{6160}(2353, \cdot)$$ n/a 432 2
6160.2.cn $$\chi_{6160}(659, \cdot)$$ n/a 1728 2
6160.2.co $$\chi_{6160}(461, \cdot)$$ n/a 1536 2
6160.2.cp $$\chi_{6160}(1541, \cdot)$$ n/a 960 2
6160.2.cq $$\chi_{6160}(419, \cdot)$$ n/a 1920 2
6160.2.cv $$\chi_{6160}(1387, \cdot)$$ n/a 1440 2
6160.2.cx $$\chi_{6160}(3277, \cdot)$$ n/a 1728 2
6160.2.da $$\chi_{6160}(573, \cdot)$$ n/a 1920 2
6160.2.dc $$\chi_{6160}(307, \cdot)$$ n/a 2288 2
6160.2.dd $$\chi_{6160}(1681, \cdot)$$ n/a 576 4
6160.2.dg $$\chi_{6160}(199, \cdot)$$ None 0 2
6160.2.dh $$\chi_{6160}(2441, \cdot)$$ None 0 2
6160.2.di $$\chi_{6160}(4289, \cdot)$$ n/a 568 2
6160.2.dj $$\chi_{6160}(3631, \cdot)$$ n/a 320 2
6160.2.dm $$\chi_{6160}(879, \cdot)$$ n/a 576 2
6160.2.dr $$\chi_{6160}(3609, \cdot)$$ None 0 2
6160.2.ds $$\chi_{6160}(5191, \cdot)$$ None 0 2
6160.2.dv $$\chi_{6160}(4841, \cdot)$$ None 0 2
6160.2.dw $$\chi_{6160}(3959, \cdot)$$ None 0 2
6160.2.dx $$\chi_{6160}(2111, \cdot)$$ n/a 384 2
6160.2.dy $$\chi_{6160}(529, \cdot)$$ n/a 480 2
6160.2.eb $$\chi_{6160}(241, \cdot)$$ n/a 384 2
6160.2.ec $$\chi_{6160}(2399, \cdot)$$ n/a 480 2
6160.2.eh $$\chi_{6160}(551, \cdot)$$ None 0 2
6160.2.ei $$\chi_{6160}(1209, \cdot)$$ None 0 2
6160.2.ej $$\chi_{6160}(239, \cdot)$$ n/a 864 4
6160.2.eo $$\chi_{6160}(1751, \cdot)$$ None 0 4
6160.2.ep $$\chi_{6160}(169, \cdot)$$ None 0 4
6160.2.es $$\chi_{6160}(41, \cdot)$$ None 0 4
6160.2.et $$\chi_{6160}(279, \cdot)$$ None 0 4
6160.2.eu $$\chi_{6160}(1791, \cdot)$$ n/a 768 4
6160.2.ev $$\chi_{6160}(1889, \cdot)$$ n/a 1136 4
6160.2.ey $$\chi_{6160}(559, \cdot)$$ n/a 1152 4
6160.2.ez $$\chi_{6160}(321, \cdot)$$ n/a 768 4
6160.2.fe $$\chi_{6160}(2169, \cdot)$$ None 0 4
6160.2.ff $$\chi_{6160}(951, \cdot)$$ None 0 4
6160.2.fi $$\chi_{6160}(519, \cdot)$$ None 0 4
6160.2.fj $$\chi_{6160}(841, \cdot)$$ None 0 4
6160.2.fk $$\chi_{6160}(449, \cdot)$$ n/a 864 4
6160.2.fl $$\chi_{6160}(1471, \cdot)$$ n/a 576 4
6160.2.fp $$\chi_{6160}(373, \cdot)$$ n/a 4576 4
6160.2.fr $$\chi_{6160}(3147, \cdot)$$ n/a 3840 4
6160.2.fs $$\chi_{6160}(3827, \cdot)$$ n/a 4576 4
6160.2.fu $$\chi_{6160}(3477, \cdot)$$ n/a 3840 4
6160.2.ga $$\chi_{6160}(859, \cdot)$$ n/a 3840 4
6160.2.gb $$\chi_{6160}(221, \cdot)$$ n/a 2560 4
6160.2.gc $$\chi_{6160}(901, \cdot)$$ n/a 3072 4
6160.2.gd $$\chi_{6160}(219, \cdot)$$ n/a 4576 4
6160.2.gf $$\chi_{6160}(2223, \cdot)$$ n/a 960 4
6160.2.gg $$\chi_{6160}(353, \cdot)$$ n/a 960 4
6160.2.gj $$\chi_{6160}(417, \cdot)$$ n/a 1136 4
6160.2.gk $$\chi_{6160}(703, \cdot)$$ n/a 1152 4
6160.2.gm $$\chi_{6160}(1033, \cdot)$$ None 0 4
6160.2.gp $$\chi_{6160}(87, \cdot)$$ None 0 4
6160.2.gq $$\chi_{6160}(23, \cdot)$$ None 0 4
6160.2.gt $$\chi_{6160}(2553, \cdot)$$ None 0 4
6160.2.gu $$\chi_{6160}(2091, \cdot)$$ n/a 2560 4
6160.2.gv $$\chi_{6160}(2069, \cdot)$$ n/a 3840 4
6160.2.gw $$\chi_{6160}(549, \cdot)$$ n/a 4576 4
6160.2.gx $$\chi_{6160}(571, \cdot)$$ n/a 3072 4
6160.2.hd $$\chi_{6160}(747, \cdot)$$ n/a 4576 4
6160.2.hf $$\chi_{6160}(397, \cdot)$$ n/a 3840 4
6160.2.hg $$\chi_{6160}(1957, \cdot)$$ n/a 4576 4
6160.2.hi $$\chi_{6160}(67, \cdot)$$ n/a 3840 4
6160.2.hk $$\chi_{6160}(81, \cdot)$$ n/a 1536 8
6160.2.hm $$\chi_{6160}(1427, \cdot)$$ n/a 9152 8
6160.2.ho $$\chi_{6160}(1637, \cdot)$$ n/a 9152 8
6160.2.hp $$\chi_{6160}(1597, \cdot)$$ n/a 6912 8
6160.2.hr $$\chi_{6160}(267, \cdot)$$ n/a 6912 8
6160.2.ht $$\chi_{6160}(1259, \cdot)$$ n/a 9152 8
6160.2.hu $$\chi_{6160}(141, \cdot)$$ n/a 4608 8
6160.2.hv $$\chi_{6160}(1581, \cdot)$$ n/a 6144 8
6160.2.hw $$\chi_{6160}(1779, \cdot)$$ n/a 6912 8
6160.2.ic $$\chi_{6160}(337, \cdot)$$ n/a 1728 8
6160.2.id $$\chi_{6160}(447, \cdot)$$ n/a 2304 8
6160.2.ig $$\chi_{6160}(687, \cdot)$$ n/a 1728 8
6160.2.ih $$\chi_{6160}(97, \cdot)$$ n/a 2272 8
6160.2.ij $$\chi_{6160}(1303, \cdot)$$ None 0 8
6160.2.im $$\chi_{6160}(377, \cdot)$$ None 0 8
6160.2.in $$\chi_{6160}(57, \cdot)$$ None 0 8
6160.2.iq $$\chi_{6160}(167, \cdot)$$ None 0 8
6160.2.iv $$\chi_{6160}(251, \cdot)$$ n/a 6144 8
6160.2.iw $$\chi_{6160}(1149, \cdot)$$ n/a 6912 8
6160.2.ix $$\chi_{6160}(349, \cdot)$$ n/a 9152 8
6160.2.iy $$\chi_{6160}(211, \cdot)$$ n/a 4608 8
6160.2.ja $$\chi_{6160}(1317, \cdot)$$ n/a 6912 8
6160.2.jc $$\chi_{6160}(603, \cdot)$$ n/a 6912 8
6160.2.jd $$\chi_{6160}(83, \cdot)$$ n/a 9152 8
6160.2.jf $$\chi_{6160}(797, \cdot)$$ n/a 9152 8
6160.2.jh $$\chi_{6160}(409, \cdot)$$ None 0 8
6160.2.ji $$\chi_{6160}(311, \cdot)$$ None 0 8
6160.2.jn $$\chi_{6160}(159, \cdot)$$ n/a 2304 8
6160.2.jo $$\chi_{6160}(481, \cdot)$$ n/a 1536 8
6160.2.jr $$\chi_{6160}(289, \cdot)$$ n/a 2272 8
6160.2.js $$\chi_{6160}(431, \cdot)$$ n/a 1536 8
6160.2.jt $$\chi_{6160}(39, \cdot)$$ None 0 8
6160.2.ju $$\chi_{6160}(361, \cdot)$$ None 0 8
6160.2.jx $$\chi_{6160}(151, \cdot)$$ None 0 8
6160.2.jy $$\chi_{6160}(9, \cdot)$$ None 0 8
6160.2.kd $$\chi_{6160}(79, \cdot)$$ n/a 2304 8
6160.2.kg $$\chi_{6160}(31, \cdot)$$ n/a 1536 8
6160.2.kh $$\chi_{6160}(129, \cdot)$$ n/a 2272 8
6160.2.ki $$\chi_{6160}(761, \cdot)$$ None 0 8
6160.2.kj $$\chi_{6160}(999, \cdot)$$ None 0 8
6160.2.km $$\chi_{6160}(443, \cdot)$$ n/a 18304 16
6160.2.ko $$\chi_{6160}(277, \cdot)$$ n/a 18304 16
6160.2.kr $$\chi_{6160}(157, \cdot)$$ n/a 18304 16
6160.2.kt $$\chi_{6160}(563, \cdot)$$ n/a 18304 16
6160.2.ku $$\chi_{6160}(51, \cdot)$$ n/a 12288 16
6160.2.kv $$\chi_{6160}(789, \cdot)$$ n/a 18304 16
6160.2.kw $$\chi_{6160}(389, \cdot)$$ n/a 18304 16
6160.2.kx $$\chi_{6160}(411, \cdot)$$ n/a 12288 16
6160.2.lc $$\chi_{6160}(313, \cdot)$$ None 0 16
6160.2.lf $$\chi_{6160}(247, \cdot)$$ None 0 16
6160.2.lg $$\chi_{6160}(327, \cdot)$$ None 0 16
6160.2.lj $$\chi_{6160}(233, \cdot)$$ None 0 16
6160.2.ll $$\chi_{6160}(607, \cdot)$$ n/a 4608 16
6160.2.lm $$\chi_{6160}(193, \cdot)$$ n/a 4544 16
6160.2.lp $$\chi_{6160}(257, \cdot)$$ n/a 4544 16
6160.2.lq $$\chi_{6160}(207, \cdot)$$ n/a 4608 16
6160.2.lw $$\chi_{6160}(459, \cdot)$$ n/a 18304 16
6160.2.lx $$\chi_{6160}(61, \cdot)$$ n/a 12288 16
6160.2.ly $$\chi_{6160}(1061, \cdot)$$ n/a 12288 16
6160.2.lz $$\chi_{6160}(59, \cdot)$$ n/a 18304 16
6160.2.ma $$\chi_{6160}(493, \cdot)$$ n/a 18304 16
6160.2.mc $$\chi_{6160}(227, \cdot)$$ n/a 18304 16
6160.2.mf $$\chi_{6160}(163, \cdot)$$ n/a 18304 16
6160.2.mh $$\chi_{6160}(557, \cdot)$$ n/a 18304 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6160))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6160)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(616))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(770))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(880))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1232))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1540))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3080))$$$$^{\oplus 2}$$