Properties

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

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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

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