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Properties

Label 4160.2
Level 4160
Weight 2
Dimension 261492
Nonzero newspaces 104
Sturm bound 2064384

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Defining parameters

Level: \( N \) = \( 4160 = 2^{6} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(2064384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4160))\).

Total New Old
Modular forms 523008 264396 258612
Cusp forms 509185 261492 247693
Eisenstein series 13823 2904 10919

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4160))\)

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
4160.2.a \(\chi_{4160}(1, \cdot)\) 4160.2.a.a 1 1
4160.2.a.b 1
4160.2.a.c 1
4160.2.a.d 1
4160.2.a.e 1
4160.2.a.f 1
4160.2.a.g 1
4160.2.a.h 1
4160.2.a.i 1
4160.2.a.j 1
4160.2.a.k 1
4160.2.a.l 1
4160.2.a.m 1
4160.2.a.n 1
4160.2.a.o 1
4160.2.a.p 1
4160.2.a.q 1
4160.2.a.r 1
4160.2.a.s 1
4160.2.a.t 1
4160.2.a.u 2
4160.2.a.v 2
4160.2.a.w 2
4160.2.a.x 2
4160.2.a.y 2
4160.2.a.z 2
4160.2.a.ba 2
4160.2.a.bb 2
4160.2.a.bc 2
4160.2.a.bd 2
4160.2.a.be 2
4160.2.a.bf 2
4160.2.a.bg 2
4160.2.a.bh 2
4160.2.a.bi 2
4160.2.a.bj 2
4160.2.a.bk 2
4160.2.a.bl 2
4160.2.a.bm 2
4160.2.a.bn 2
4160.2.a.bo 3
4160.2.a.bp 3
4160.2.a.bq 3
4160.2.a.br 3
4160.2.a.bs 4
4160.2.a.bt 4
4160.2.a.bu 4
4160.2.a.bv 4
4160.2.a.bw 4
4160.2.a.bx 4
4160.2.d \(\chi_{4160}(3329, \cdot)\) n/a 144 1
4160.2.e \(\chi_{4160}(3041, \cdot)\) n/a 112 1
4160.2.f \(\chi_{4160}(129, \cdot)\) n/a 164 1
4160.2.g \(\chi_{4160}(2081, \cdot)\) 4160.2.g.a 2 1
4160.2.g.b 2
4160.2.g.c 6
4160.2.g.d 6
4160.2.g.e 8
4160.2.g.f 8
4160.2.g.g 16
4160.2.g.h 16
4160.2.g.i 16
4160.2.g.j 16
4160.2.j \(\chi_{4160}(1249, \cdot)\) n/a 144 1
4160.2.k \(\chi_{4160}(961, \cdot)\) n/a 112 1
4160.2.p \(\chi_{4160}(2209, \cdot)\) n/a 168 1
4160.2.q \(\chi_{4160}(321, \cdot)\) n/a 224 2
4160.2.s \(\chi_{4160}(177, \cdot)\) n/a 328 2
4160.2.u \(\chi_{4160}(2111, \cdot)\) n/a 224 2
4160.2.v \(\chi_{4160}(1327, \cdot)\) n/a 288 2
4160.2.y \(\chi_{4160}(2287, \cdot)\) n/a 328 2
4160.2.z \(\chi_{4160}(3359, \cdot)\) n/a 336 2
4160.2.bb \(\chi_{4160}(593, \cdot)\) n/a 328 2
4160.2.be \(\chi_{4160}(1169, \cdot)\) n/a 328 2
4160.2.bg \(\chi_{4160}(577, \cdot)\) n/a 328 2
4160.2.bi \(\chi_{4160}(1633, \cdot)\) n/a 336 2
4160.2.bj \(\chi_{4160}(1041, \cdot)\) n/a 192 2
4160.2.bm \(\chi_{4160}(1071, \cdot)\) n/a 224 2
4160.2.bp \(\chi_{4160}(703, \cdot)\) n/a 288 2
4160.2.bq \(\chi_{4160}(1247, \cdot)\) n/a 336 2
4160.2.bs \(\chi_{4160}(239, \cdot)\) n/a 328 2
4160.2.bt \(\chi_{4160}(1711, \cdot)\) n/a 224 2
4160.2.bv \(\chi_{4160}(1663, \cdot)\) n/a 328 2
4160.2.bw \(\chi_{4160}(287, \cdot)\) n/a 288 2
4160.2.bz \(\chi_{4160}(879, \cdot)\) n/a 328 2
4160.2.cc \(\chi_{4160}(209, \cdot)\) n/a 288 2
4160.2.cd \(\chi_{4160}(1217, \cdot)\) n/a 328 2
4160.2.cf \(\chi_{4160}(993, \cdot)\) n/a 336 2
4160.2.ch \(\chi_{4160}(2001, \cdot)\) n/a 224 2
4160.2.cj \(\chi_{4160}(2033, \cdot)\) n/a 328 2
4160.2.cm \(\chi_{4160}(31, \cdot)\) n/a 224 2
4160.2.cn \(\chi_{4160}(3407, \cdot)\) n/a 288 2
4160.2.cq \(\chi_{4160}(207, \cdot)\) n/a 328 2
4160.2.cr \(\chi_{4160}(1279, \cdot)\) n/a 328 2
4160.2.cu \(\chi_{4160}(1617, \cdot)\) n/a 328 2
4160.2.cv \(\chi_{4160}(1889, \cdot)\) n/a 336 2
4160.2.da \(\chi_{4160}(641, \cdot)\) n/a 224 2
4160.2.db \(\chi_{4160}(289, \cdot)\) n/a 336 2
4160.2.de \(\chi_{4160}(1121, \cdot)\) n/a 224 2
4160.2.df \(\chi_{4160}(1089, \cdot)\) n/a 328 2
4160.2.dg \(\chi_{4160}(2721, \cdot)\) n/a 224 2
4160.2.dh \(\chi_{4160}(2369, \cdot)\) n/a 328 2
4160.2.dk \(\chi_{4160}(1399, \cdot)\) None 0 4
4160.2.dm \(\chi_{4160}(1223, \cdot)\) None 0 4
4160.2.dp \(\chi_{4160}(1143, \cdot)\) None 0 4
4160.2.dr \(\chi_{4160}(1191, \cdot)\) None 0 4
4160.2.ds \(\chi_{4160}(441, \cdot)\) None 0 4
4160.2.dv \(\chi_{4160}(521, \cdot)\) None 0 4
4160.2.dw \(\chi_{4160}(473, \cdot)\) None 0 4
4160.2.dz \(\chi_{4160}(1097, \cdot)\) None 0 4
4160.2.eb \(\chi_{4160}(697, \cdot)\) None 0 4
4160.2.ec \(\chi_{4160}(57, \cdot)\) None 0 4
4160.2.ef \(\chi_{4160}(649, \cdot)\) None 0 4
4160.2.eg \(\chi_{4160}(729, \cdot)\) None 0 4
4160.2.ej \(\chi_{4160}(359, \cdot)\) None 0 4
4160.2.el \(\chi_{4160}(103, \cdot)\) None 0 4
4160.2.em \(\chi_{4160}(183, \cdot)\) None 0 4
4160.2.eo \(\chi_{4160}(151, \cdot)\) None 0 4
4160.2.eq \(\chi_{4160}(977, \cdot)\) n/a 656 4
4160.2.et \(\chi_{4160}(319, \cdot)\) n/a 656 4
4160.2.ev \(\chi_{4160}(2447, \cdot)\) n/a 656 4
4160.2.ew \(\chi_{4160}(303, \cdot)\) n/a 656 4
4160.2.ey \(\chi_{4160}(1311, \cdot)\) n/a 448 4
4160.2.fb \(\chi_{4160}(657, \cdot)\) n/a 656 4
4160.2.fd \(\chi_{4160}(881, \cdot)\) n/a 448 4
4160.2.ff \(\chi_{4160}(353, \cdot)\) n/a 672 4
4160.2.fh \(\chi_{4160}(513, \cdot)\) n/a 656 4
4160.2.fi \(\chi_{4160}(529, \cdot)\) n/a 656 4
4160.2.fk \(\chi_{4160}(1519, \cdot)\) n/a 656 4
4160.2.fm \(\chi_{4160}(607, \cdot)\) n/a 672 4
4160.2.fn \(\chi_{4160}(127, \cdot)\) n/a 656 4
4160.2.fq \(\chi_{4160}(111, \cdot)\) n/a 448 4
4160.2.ft \(\chi_{4160}(1359, \cdot)\) n/a 656 4
4160.2.fw \(\chi_{4160}(543, \cdot)\) n/a 672 4
4160.2.fx \(\chi_{4160}(1023, \cdot)\) n/a 656 4
4160.2.fz \(\chi_{4160}(271, \cdot)\) n/a 448 4
4160.2.gb \(\chi_{4160}(81, \cdot)\) n/a 448 4
4160.2.gc \(\chi_{4160}(33, \cdot)\) n/a 672 4
4160.2.ge \(\chi_{4160}(193, \cdot)\) n/a 656 4
4160.2.gg \(\chi_{4160}(49, \cdot)\) n/a 656 4
4160.2.gj \(\chi_{4160}(1137, \cdot)\) n/a 656 4
4160.2.gl \(\chi_{4160}(479, \cdot)\) n/a 672 4
4160.2.gn \(\chi_{4160}(367, \cdot)\) n/a 656 4
4160.2.go \(\chi_{4160}(1967, \cdot)\) n/a 656 4
4160.2.gq \(\chi_{4160}(1151, \cdot)\) n/a 448 4
4160.2.gs \(\chi_{4160}(817, \cdot)\) n/a 656 4
4160.2.gu \(\chi_{4160}(363, \cdot)\) n/a 5344 8
4160.2.gx \(\chi_{4160}(333, \cdot)\) n/a 5344 8
4160.2.gy \(\chi_{4160}(437, \cdot)\) n/a 5344 8
4160.2.ha \(\chi_{4160}(443, \cdot)\) n/a 4608 8
4160.2.hd \(\chi_{4160}(261, \cdot)\) n/a 3072 8
4160.2.he \(\chi_{4160}(469, \cdot)\) n/a 4608 8
4160.2.hh \(\chi_{4160}(811, \cdot)\) n/a 3584 8
4160.2.hi \(\chi_{4160}(499, \cdot)\) n/a 5344 8
4160.2.hk \(\chi_{4160}(99, \cdot)\) n/a 5344 8
4160.2.hn \(\chi_{4160}(291, \cdot)\) n/a 3584 8
4160.2.hp \(\chi_{4160}(389, \cdot)\) n/a 5344 8
4160.2.hq \(\chi_{4160}(181, \cdot)\) n/a 3584 8
4160.2.hs \(\chi_{4160}(883, \cdot)\) n/a 5344 8
4160.2.hv \(\chi_{4160}(317, \cdot)\) n/a 5344 8
4160.2.hw \(\chi_{4160}(213, \cdot)\) n/a 5344 8
4160.2.hy \(\chi_{4160}(27, \cdot)\) n/a 4608 8
4160.2.ib \(\chi_{4160}(71, \cdot)\) None 0 8
4160.2.ic \(\chi_{4160}(503, \cdot)\) None 0 8
4160.2.if \(\chi_{4160}(407, \cdot)\) None 0 8
4160.2.ig \(\chi_{4160}(119, \cdot)\) None 0 8
4160.2.ii \(\chi_{4160}(329, \cdot)\) None 0 8
4160.2.il \(\chi_{4160}(9, \cdot)\) None 0 8
4160.2.in \(\chi_{4160}(553, \cdot)\) None 0 8
4160.2.io \(\chi_{4160}(873, \cdot)\) None 0 8
4160.2.iq \(\chi_{4160}(457, \cdot)\) None 0 8
4160.2.it \(\chi_{4160}(137, \cdot)\) None 0 8
4160.2.iv \(\chi_{4160}(121, \cdot)\) None 0 8
4160.2.iw \(\chi_{4160}(601, \cdot)\) None 0 8
4160.2.iy \(\chi_{4160}(951, \cdot)\) None 0 8
4160.2.jb \(\chi_{4160}(23, \cdot)\) None 0 8
4160.2.jc \(\chi_{4160}(87, \cdot)\) None 0 8
4160.2.jf \(\chi_{4160}(1159, \cdot)\) None 0 8
4160.2.jh \(\chi_{4160}(563, \cdot)\) n/a 10688 16
4160.2.jj \(\chi_{4160}(397, \cdot)\) n/a 10688 16
4160.2.jk \(\chi_{4160}(293, \cdot)\) n/a 10688 16
4160.2.jn \(\chi_{4160}(3, \cdot)\) n/a 10688 16
4160.2.jp \(\chi_{4160}(29, \cdot)\) n/a 10688 16
4160.2.jq \(\chi_{4160}(61, \cdot)\) n/a 7168 16
4160.2.jt \(\chi_{4160}(19, \cdot)\) n/a 10688 16
4160.2.ju \(\chi_{4160}(171, \cdot)\) n/a 7168 16
4160.2.jw \(\chi_{4160}(11, \cdot)\) n/a 7168 16
4160.2.jz \(\chi_{4160}(379, \cdot)\) n/a 10688 16
4160.2.kb \(\chi_{4160}(101, \cdot)\) n/a 7168 16
4160.2.kc \(\chi_{4160}(69, \cdot)\) n/a 10688 16
4160.2.kf \(\chi_{4160}(43, \cdot)\) n/a 10688 16
4160.2.kh \(\chi_{4160}(37, \cdot)\) n/a 10688 16
4160.2.ki \(\chi_{4160}(197, \cdot)\) n/a 10688 16
4160.2.kl \(\chi_{4160}(523, \cdot)\) n/a 10688 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1040))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4160))\)\(^{\oplus 1}\)