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Properties

Label 4560.2
Level 4560
Weight 2
Dimension 211736
Nonzero newspaces 84
Sturm bound 2211840

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Defining parameters

Level: \( N \) = \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(2211840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4560))\).

Total New Old
Modular forms 561024 213568 347456
Cusp forms 544897 211736 333161
Eisenstein series 16127 1832 14295

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4560))\)

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
4560.2.a \(\chi_{4560}(1, \cdot)\) 4560.2.a.a 1 1
4560.2.a.b 1
4560.2.a.c 1
4560.2.a.d 1
4560.2.a.e 1
4560.2.a.f 1
4560.2.a.g 1
4560.2.a.h 1
4560.2.a.i 1
4560.2.a.j 1
4560.2.a.k 1
4560.2.a.l 1
4560.2.a.m 1
4560.2.a.n 1
4560.2.a.o 1
4560.2.a.p 1
4560.2.a.q 1
4560.2.a.r 1
4560.2.a.s 1
4560.2.a.t 1
4560.2.a.u 1
4560.2.a.v 1
4560.2.a.w 1
4560.2.a.x 1
4560.2.a.y 1
4560.2.a.z 1
4560.2.a.ba 1
4560.2.a.bb 1
4560.2.a.bc 1
4560.2.a.bd 1
4560.2.a.be 2
4560.2.a.bf 2
4560.2.a.bg 2
4560.2.a.bh 2
4560.2.a.bi 2
4560.2.a.bj 2
4560.2.a.bk 2
4560.2.a.bl 2
4560.2.a.bm 2
4560.2.a.bn 2
4560.2.a.bo 2
4560.2.a.bp 2
4560.2.a.bq 3
4560.2.a.br 3
4560.2.a.bs 3
4560.2.a.bt 3
4560.2.a.bu 3
4560.2.a.bv 3
4560.2.c \(\chi_{4560}(2471, \cdot)\) None 0 1
4560.2.d \(\chi_{4560}(2431, \cdot)\) 4560.2.d.a 2 1
4560.2.d.b 2
4560.2.d.c 2
4560.2.d.d 2
4560.2.d.e 6
4560.2.d.f 6
4560.2.d.g 6
4560.2.d.h 6
4560.2.d.i 12
4560.2.d.j 12
4560.2.d.k 12
4560.2.d.l 12
4560.2.f \(\chi_{4560}(1369, \cdot)\) None 0 1
4560.2.i \(\chi_{4560}(2849, \cdot)\) n/a 236 1
4560.2.j \(\chi_{4560}(3649, \cdot)\) n/a 108 1
4560.2.m \(\chi_{4560}(569, \cdot)\) None 0 1
4560.2.o \(\chi_{4560}(191, \cdot)\) n/a 144 1
4560.2.p \(\chi_{4560}(151, \cdot)\) None 0 1
4560.2.r \(\chi_{4560}(3761, \cdot)\) n/a 160 1
4560.2.u \(\chi_{4560}(2281, \cdot)\) None 0 1
4560.2.w \(\chi_{4560}(1519, \cdot)\) n/a 120 1
4560.2.x \(\chi_{4560}(1559, \cdot)\) None 0 1
4560.2.ba \(\chi_{4560}(3799, \cdot)\) None 0 1
4560.2.bb \(\chi_{4560}(3839, \cdot)\) n/a 216 1
4560.2.bd \(\chi_{4560}(1481, \cdot)\) None 0 1
4560.2.bg \(\chi_{4560}(961, \cdot)\) n/a 160 2
4560.2.bi \(\chi_{4560}(379, \cdot)\) n/a 960 2
4560.2.bj \(\chi_{4560}(341, \cdot)\) n/a 1280 2
4560.2.bm \(\chi_{4560}(1141, \cdot)\) n/a 576 2
4560.2.bn \(\chi_{4560}(419, \cdot)\) n/a 1728 2
4560.2.bp \(\chi_{4560}(1177, \cdot)\) None 0 2
4560.2.bs \(\chi_{4560}(2623, \cdot)\) n/a 216 2
4560.2.bu \(\chi_{4560}(1217, \cdot)\) n/a 432 2
4560.2.bv \(\chi_{4560}(1367, \cdot)\) None 0 2
4560.2.by \(\chi_{4560}(3307, \cdot)\) n/a 864 2
4560.2.ca \(\chi_{4560}(2317, \cdot)\) n/a 960 2
4560.2.cb \(\chi_{4560}(227, \cdot)\) n/a 1904 2
4560.2.cd \(\chi_{4560}(2357, \cdot)\) n/a 1728 2
4560.2.cf \(\chi_{4560}(1027, \cdot)\) n/a 864 2
4560.2.ch \(\chi_{4560}(37, \cdot)\) n/a 960 2
4560.2.ck \(\chi_{4560}(2507, \cdot)\) n/a 1904 2
4560.2.cm \(\chi_{4560}(77, \cdot)\) n/a 1728 2
4560.2.cn \(\chi_{4560}(1673, \cdot)\) None 0 2
4560.2.cq \(\chi_{4560}(1823, \cdot)\) n/a 480 2
4560.2.cs \(\chi_{4560}(1633, \cdot)\) n/a 240 2
4560.2.ct \(\chi_{4560}(343, \cdot)\) None 0 2
4560.2.cv \(\chi_{4560}(1331, \cdot)\) n/a 1152 2
4560.2.cy \(\chi_{4560}(229, \cdot)\) n/a 864 2
4560.2.cz \(\chi_{4560}(1709, \cdot)\) n/a 1904 2
4560.2.dc \(\chi_{4560}(1291, \cdot)\) n/a 640 2
4560.2.dd \(\chi_{4560}(449, \cdot)\) n/a 472 2
4560.2.dg \(\chi_{4560}(2329, \cdot)\) None 0 2
4560.2.di \(\chi_{4560}(31, \cdot)\) n/a 160 2
4560.2.dj \(\chi_{4560}(311, \cdot)\) None 0 2
4560.2.dm \(\chi_{4560}(2311, \cdot)\) None 0 2
4560.2.dn \(\chi_{4560}(1151, \cdot)\) n/a 320 2
4560.2.dp \(\chi_{4560}(2729, \cdot)\) None 0 2
4560.2.ds \(\chi_{4560}(49, \cdot)\) n/a 240 2
4560.2.du \(\chi_{4560}(2519, \cdot)\) None 0 2
4560.2.dv \(\chi_{4560}(559, \cdot)\) n/a 240 2
4560.2.dx \(\chi_{4560}(121, \cdot)\) None 0 2
4560.2.ea \(\chi_{4560}(1361, \cdot)\) n/a 320 2
4560.2.ed \(\chi_{4560}(521, \cdot)\) None 0 2
4560.2.ef \(\chi_{4560}(239, \cdot)\) n/a 480 2
4560.2.eg \(\chi_{4560}(1399, \cdot)\) None 0 2
4560.2.ei \(\chi_{4560}(481, \cdot)\) n/a 480 6
4560.2.ej \(\chi_{4560}(539, \cdot)\) n/a 3808 4
4560.2.em \(\chi_{4560}(1261, \cdot)\) n/a 1280 4
4560.2.en \(\chi_{4560}(221, \cdot)\) n/a 2560 4
4560.2.eq \(\chi_{4560}(259, \cdot)\) n/a 1920 4
4560.2.es \(\chi_{4560}(407, \cdot)\) None 0 4
4560.2.et \(\chi_{4560}(353, \cdot)\) n/a 944 4
4560.2.ev \(\chi_{4560}(463, \cdot)\) n/a 480 4
4560.2.ey \(\chi_{4560}(217, \cdot)\) None 0 4
4560.2.fa \(\chi_{4560}(2197, \cdot)\) n/a 1920 4
4560.2.fc \(\chi_{4560}(1987, \cdot)\) n/a 1920 4
4560.2.fd \(\chi_{4560}(1037, \cdot)\) n/a 3808 4
4560.2.ff \(\chi_{4560}(107, \cdot)\) n/a 3808 4
4560.2.fh \(\chi_{4560}(373, \cdot)\) n/a 1920 4
4560.2.fj \(\chi_{4560}(163, \cdot)\) n/a 1920 4
4560.2.fm \(\chi_{4560}(197, \cdot)\) n/a 3808 4
4560.2.fo \(\chi_{4560}(2387, \cdot)\) n/a 3808 4
4560.2.fq \(\chi_{4560}(7, \cdot)\) None 0 4
4560.2.fr \(\chi_{4560}(673, \cdot)\) n/a 480 4
4560.2.ft \(\chi_{4560}(863, \cdot)\) n/a 960 4
4560.2.fw \(\chi_{4560}(1337, \cdot)\) None 0 4
4560.2.fy \(\chi_{4560}(331, \cdot)\) n/a 1280 4
4560.2.fz \(\chi_{4560}(749, \cdot)\) n/a 3808 4
4560.2.gc \(\chi_{4560}(349, \cdot)\) n/a 1920 4
4560.2.gd \(\chi_{4560}(11, \cdot)\) n/a 2560 4
4560.2.gg \(\chi_{4560}(439, \cdot)\) None 0 6
4560.2.gj \(\chi_{4560}(479, \cdot)\) n/a 1440 6
4560.2.gk \(\chi_{4560}(41, \cdot)\) None 0 6
4560.2.gn \(\chi_{4560}(841, \cdot)\) None 0 6
4560.2.go \(\chi_{4560}(79, \cdot)\) n/a 720 6
4560.2.gr \(\chi_{4560}(401, \cdot)\) n/a 960 6
4560.2.gs \(\chi_{4560}(119, \cdot)\) None 0 6
4560.2.gv \(\chi_{4560}(289, \cdot)\) n/a 720 6
4560.2.gw \(\chi_{4560}(1351, \cdot)\) None 0 6
4560.2.gz \(\chi_{4560}(89, \cdot)\) None 0 6
4560.2.ha \(\chi_{4560}(671, \cdot)\) n/a 960 6
4560.2.hd \(\chi_{4560}(751, \cdot)\) n/a 480 6
4560.2.he \(\chi_{4560}(169, \cdot)\) None 0 6
4560.2.hh \(\chi_{4560}(1031, \cdot)\) None 0 6
4560.2.hi \(\chi_{4560}(1169, \cdot)\) n/a 1416 6
4560.2.hk \(\chi_{4560}(709, \cdot)\) n/a 5760 12
4560.2.hm \(\chi_{4560}(91, \cdot)\) n/a 3840 12
4560.2.ho \(\chi_{4560}(131, \cdot)\) n/a 7680 12
4560.2.hq \(\chi_{4560}(29, \cdot)\) n/a 11424 12
4560.2.ht \(\chi_{4560}(143, \cdot)\) n/a 2880 12
4560.2.hu \(\chi_{4560}(137, \cdot)\) None 0 12
4560.2.hx \(\chi_{4560}(97, \cdot)\) n/a 1440 12
4560.2.hy \(\chi_{4560}(727, \cdot)\) None 0 12
4560.2.ia \(\chi_{4560}(917, \cdot)\) n/a 11424 12
4560.2.ic \(\chi_{4560}(203, \cdot)\) n/a 11424 12
4560.2.if \(\chi_{4560}(827, \cdot)\) n/a 11424 12
4560.2.ih \(\chi_{4560}(557, \cdot)\) n/a 11424 12
4560.2.ii \(\chi_{4560}(637, \cdot)\) n/a 5760 12
4560.2.ik \(\chi_{4560}(187, \cdot)\) n/a 5760 12
4560.2.in \(\chi_{4560}(43, \cdot)\) n/a 5760 12
4560.2.ip \(\chi_{4560}(13, \cdot)\) n/a 5760 12
4560.2.iq \(\chi_{4560}(17, \cdot)\) n/a 2832 12
4560.2.it \(\chi_{4560}(167, \cdot)\) None 0 12
4560.2.iu \(\chi_{4560}(367, \cdot)\) n/a 1440 12
4560.2.ix \(\chi_{4560}(553, \cdot)\) None 0 12
4560.2.iz \(\chi_{4560}(979, \cdot)\) n/a 5760 12
4560.2.jb \(\chi_{4560}(61, \cdot)\) n/a 3840 12
4560.2.jd \(\chi_{4560}(941, \cdot)\) n/a 7680 12
4560.2.jf \(\chi_{4560}(899, \cdot)\) n/a 11424 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4560))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4560)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2280))\)\(^{\oplus 2}\)