Properties

Label 6080.2
Level 6080
Weight 2
Dimension 564828
Nonzero newspaces 84
Sturm bound 4423680

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Defining parameters

Level: \( N \) = \( 6080 = 2^{6} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(4423680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6080))\).

Total New Old
Modular forms 1116288 569316 546972
Cusp forms 1095553 564828 530725
Eisenstein series 20735 4488 16247

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6080))\)

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
6080.2.a \(\chi_{6080}(1, \cdot)\) 6080.2.a.a 1 1
6080.2.a.b 1
6080.2.a.c 1
6080.2.a.d 1
6080.2.a.e 1
6080.2.a.f 1
6080.2.a.g 1
6080.2.a.h 1
6080.2.a.i 1
6080.2.a.j 1
6080.2.a.k 1
6080.2.a.l 1
6080.2.a.m 1
6080.2.a.n 1
6080.2.a.o 1
6080.2.a.p 1
6080.2.a.q 1
6080.2.a.r 1
6080.2.a.s 1
6080.2.a.t 1
6080.2.a.u 1
6080.2.a.v 1
6080.2.a.w 1
6080.2.a.x 1
6080.2.a.y 2
6080.2.a.z 2
6080.2.a.ba 2
6080.2.a.bb 2
6080.2.a.bc 2
6080.2.a.bd 2
6080.2.a.be 2
6080.2.a.bf 2
6080.2.a.bg 2
6080.2.a.bh 2
6080.2.a.bi 2
6080.2.a.bj 2
6080.2.a.bk 2
6080.2.a.bl 2
6080.2.a.bm 3
6080.2.a.bn 3
6080.2.a.bo 3
6080.2.a.bp 3
6080.2.a.bq 3
6080.2.a.br 3
6080.2.a.bs 3
6080.2.a.bt 3
6080.2.a.bu 3
6080.2.a.bv 3
6080.2.a.bw 3
6080.2.a.bx 3
6080.2.a.by 3
6080.2.a.bz 3
6080.2.a.ca 3
6080.2.a.cb 3
6080.2.a.cc 4
6080.2.a.cd 4
6080.2.a.ce 4
6080.2.a.cf 4
6080.2.a.cg 4
6080.2.a.ch 4
6080.2.a.ci 5
6080.2.a.cj 5
6080.2.a.ck 5
6080.2.a.cl 5
6080.2.d \(\chi_{6080}(3649, \cdot)\) n/a 216 1
6080.2.e \(\chi_{6080}(5471, \cdot)\) n/a 160 1
6080.2.f \(\chi_{6080}(3041, \cdot)\) n/a 144 1
6080.2.g \(\chi_{6080}(6079, \cdot)\) n/a 236 1
6080.2.j \(\chi_{6080}(2431, \cdot)\) n/a 160 1
6080.2.k \(\chi_{6080}(609, \cdot)\) n/a 216 1
6080.2.p \(\chi_{6080}(3039, \cdot)\) n/a 240 1
6080.2.q \(\chi_{6080}(961, \cdot)\) n/a 320 2
6080.2.r \(\chi_{6080}(113, \cdot)\) n/a 472 2
6080.2.t \(\chi_{6080}(1103, \cdot)\) n/a 432 2
6080.2.w \(\chi_{6080}(1519, \cdot)\) n/a 472 2
6080.2.y \(\chi_{6080}(1521, \cdot)\) n/a 288 2
6080.2.bb \(\chi_{6080}(417, \cdot)\) n/a 480 2
6080.2.bc \(\chi_{6080}(1407, \cdot)\) n/a 432 2
6080.2.bd \(\chi_{6080}(3457, \cdot)\) n/a 472 2
6080.2.be \(\chi_{6080}(4447, \cdot)\) n/a 432 2
6080.2.bi \(\chi_{6080}(2129, \cdot)\) n/a 432 2
6080.2.bk \(\chi_{6080}(911, \cdot)\) n/a 320 2
6080.2.bl \(\chi_{6080}(4143, \cdot)\) n/a 432 2
6080.2.bn \(\chi_{6080}(3153, \cdot)\) n/a 472 2
6080.2.bp \(\chi_{6080}(1569, \cdot)\) n/a 480 2
6080.2.bq \(\chi_{6080}(1471, \cdot)\) n/a 320 2
6080.2.bv \(\chi_{6080}(2079, \cdot)\) n/a 480 2
6080.2.by \(\chi_{6080}(31, \cdot)\) n/a 320 2
6080.2.bz \(\chi_{6080}(3009, \cdot)\) n/a 472 2
6080.2.ca \(\chi_{6080}(639, \cdot)\) n/a 472 2
6080.2.cb \(\chi_{6080}(2401, \cdot)\) n/a 320 2
6080.2.ce \(\chi_{6080}(873, \cdot)\) None 0 4
6080.2.cf \(\chi_{6080}(1863, \cdot)\) None 0 4
6080.2.ck \(\chi_{6080}(151, \cdot)\) None 0 4
6080.2.cl \(\chi_{6080}(761, \cdot)\) None 0 4
6080.2.co \(\chi_{6080}(1369, \cdot)\) None 0 4
6080.2.cp \(\chi_{6080}(759, \cdot)\) None 0 4
6080.2.cq \(\chi_{6080}(343, \cdot)\) None 0 4
6080.2.cr \(\chi_{6080}(2393, \cdot)\) None 0 4
6080.2.cu \(\chi_{6080}(321, \cdot)\) n/a 960 6
6080.2.cv \(\chi_{6080}(2193, \cdot)\) n/a 944 4
6080.2.cx \(\chi_{6080}(847, \cdot)\) n/a 944 4
6080.2.da \(\chi_{6080}(881, \cdot)\) n/a 640 4
6080.2.dc \(\chi_{6080}(559, \cdot)\) n/a 944 4
6080.2.dd \(\chi_{6080}(673, \cdot)\) n/a 960 4
6080.2.de \(\chi_{6080}(767, \cdot)\) n/a 944 4
6080.2.dj \(\chi_{6080}(2497, \cdot)\) n/a 944 4
6080.2.dk \(\chi_{6080}(543, \cdot)\) n/a 960 4
6080.2.dm \(\chi_{6080}(1551, \cdot)\) n/a 640 4
6080.2.do \(\chi_{6080}(49, \cdot)\) n/a 944 4
6080.2.dp \(\chi_{6080}(463, \cdot)\) n/a 944 4
6080.2.dr \(\chi_{6080}(753, \cdot)\) n/a 944 4
6080.2.dv \(\chi_{6080}(797, \cdot)\) n/a 7648 8
6080.2.dw \(\chi_{6080}(1027, \cdot)\) n/a 6912 8
6080.2.dx \(\chi_{6080}(379, \cdot)\) n/a 7648 8
6080.2.dy \(\chi_{6080}(381, \cdot)\) n/a 4608 8
6080.2.dz \(\chi_{6080}(229, \cdot)\) n/a 6912 8
6080.2.ea \(\chi_{6080}(531, \cdot)\) n/a 5120 8
6080.2.eh \(\chi_{6080}(267, \cdot)\) n/a 6912 8
6080.2.ei \(\chi_{6080}(37, \cdot)\) n/a 7648 8
6080.2.ej \(\chi_{6080}(1439, \cdot)\) n/a 1440 6
6080.2.eo \(\chi_{6080}(161, \cdot)\) n/a 960 6
6080.2.ep \(\chi_{6080}(319, \cdot)\) n/a 1416 6
6080.2.es \(\chi_{6080}(769, \cdot)\) n/a 1416 6
6080.2.et \(\chi_{6080}(991, \cdot)\) n/a 960 6
6080.2.eu \(\chi_{6080}(831, \cdot)\) n/a 960 6
6080.2.ev \(\chi_{6080}(289, \cdot)\) n/a 1440 6
6080.2.ey \(\chi_{6080}(87, \cdot)\) None 0 8
6080.2.ez \(\chi_{6080}(217, \cdot)\) None 0 8
6080.2.fe \(\chi_{6080}(1319, \cdot)\) None 0 8
6080.2.ff \(\chi_{6080}(729, \cdot)\) None 0 8
6080.2.fi \(\chi_{6080}(121, \cdot)\) None 0 8
6080.2.fj \(\chi_{6080}(711, \cdot)\) None 0 8
6080.2.fk \(\chi_{6080}(297, \cdot)\) None 0 8
6080.2.fl \(\chi_{6080}(7, \cdot)\) None 0 8
6080.2.fo \(\chi_{6080}(529, \cdot)\) n/a 2832 12
6080.2.fp \(\chi_{6080}(431, \cdot)\) n/a 1920 12
6080.2.fu \(\chi_{6080}(193, \cdot)\) n/a 2832 12
6080.2.fv \(\chi_{6080}(1183, \cdot)\) n/a 2880 12
6080.2.fy \(\chi_{6080}(207, \cdot)\) n/a 2832 12
6080.2.fz \(\chi_{6080}(497, \cdot)\) n/a 2832 12
6080.2.gc \(\chi_{6080}(337, \cdot)\) n/a 2832 12
6080.2.gd \(\chi_{6080}(47, \cdot)\) n/a 2832 12
6080.2.gg \(\chi_{6080}(33, \cdot)\) n/a 2880 12
6080.2.gh \(\chi_{6080}(63, \cdot)\) n/a 2832 12
6080.2.gi \(\chi_{6080}(81, \cdot)\) n/a 1920 12
6080.2.gj \(\chi_{6080}(79, \cdot)\) n/a 2832 12
6080.2.go \(\chi_{6080}(597, \cdot)\) n/a 15296 16
6080.2.gp \(\chi_{6080}(83, \cdot)\) n/a 15296 16
6080.2.gq \(\chi_{6080}(331, \cdot)\) n/a 10240 16
6080.2.gr \(\chi_{6080}(349, \cdot)\) n/a 15296 16
6080.2.gs \(\chi_{6080}(501, \cdot)\) n/a 10240 16
6080.2.gt \(\chi_{6080}(179, \cdot)\) n/a 15296 16
6080.2.ha \(\chi_{6080}(387, \cdot)\) n/a 15296 16
6080.2.hb \(\chi_{6080}(293, \cdot)\) n/a 15296 16
6080.2.he \(\chi_{6080}(793, \cdot)\) None 0 24
6080.2.hf \(\chi_{6080}(23, \cdot)\) None 0 24
6080.2.hg \(\chi_{6080}(441, \cdot)\) None 0 24
6080.2.hh \(\chi_{6080}(279, \cdot)\) None 0 24
6080.2.hi \(\chi_{6080}(9, \cdot)\) None 0 24
6080.2.hj \(\chi_{6080}(71, \cdot)\) None 0 24
6080.2.hq \(\chi_{6080}(263, \cdot)\) None 0 24
6080.2.hr \(\chi_{6080}(393, \cdot)\) None 0 24
6080.2.hs \(\chi_{6080}(13, \cdot)\) n/a 45888 48
6080.2.ht \(\chi_{6080}(43, \cdot)\) n/a 45888 48
6080.2.hy \(\chi_{6080}(53, \cdot)\) n/a 45888 48
6080.2.hz \(\chi_{6080}(187, \cdot)\) n/a 45888 48
6080.2.ic \(\chi_{6080}(59, \cdot)\) n/a 45888 48
6080.2.id \(\chi_{6080}(51, \cdot)\) n/a 30720 48
6080.2.ie \(\chi_{6080}(149, \cdot)\) n/a 45888 48
6080.2.if \(\chi_{6080}(61, \cdot)\) n/a 30720 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6080)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1520))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3040))\)\(^{\oplus 2}\)