Properties

Label 5472.2
Level 5472
Weight 2
Dimension 365778
Nonzero newspaces 96
Sturm bound 3317760

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Defining parameters

Level: \( N \) = \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(3317760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5472))\).

Total New Old
Modular forms 838656 368838 469818
Cusp forms 820225 365778 454447
Eisenstein series 18431 3060 15371

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5472))\)

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
5472.2.a \(\chi_{5472}(1, \cdot)\) 5472.2.a.a 1 1
5472.2.a.b 1
5472.2.a.c 1
5472.2.a.d 1
5472.2.a.e 1
5472.2.a.f 1
5472.2.a.g 1
5472.2.a.h 1
5472.2.a.i 1
5472.2.a.j 1
5472.2.a.k 1
5472.2.a.l 1
5472.2.a.m 1
5472.2.a.n 1
5472.2.a.o 1
5472.2.a.p 1
5472.2.a.q 1
5472.2.a.r 1
5472.2.a.s 1
5472.2.a.t 1
5472.2.a.u 1
5472.2.a.v 1
5472.2.a.w 2
5472.2.a.x 2
5472.2.a.y 2
5472.2.a.z 2
5472.2.a.ba 2
5472.2.a.bb 2
5472.2.a.bc 2
5472.2.a.bd 2
5472.2.a.be 2
5472.2.a.bf 2
5472.2.a.bg 2
5472.2.a.bh 2
5472.2.a.bi 2
5472.2.a.bj 2
5472.2.a.bk 2
5472.2.a.bl 2
5472.2.a.bm 3
5472.2.a.bn 3
5472.2.a.bo 3
5472.2.a.bp 3
5472.2.a.bq 4
5472.2.a.br 4
5472.2.a.bs 4
5472.2.a.bt 4
5472.2.a.bu 4
5472.2.a.bv 4
5472.2.d \(\chi_{5472}(2015, \cdot)\) 5472.2.d.a 4 1
5472.2.d.b 4
5472.2.d.c 4
5472.2.d.d 8
5472.2.d.e 8
5472.2.d.f 8
5472.2.d.g 16
5472.2.d.h 20
5472.2.e \(\chi_{5472}(5167, \cdot)\) 5472.2.e.a 2 1
5472.2.e.b 4
5472.2.e.c 8
5472.2.e.d 8
5472.2.e.e 12
5472.2.e.f 24
5472.2.e.g 40
5472.2.f \(\chi_{5472}(1025, \cdot)\) 5472.2.f.a 20 1
5472.2.f.b 20
5472.2.f.c 20
5472.2.f.d 20
5472.2.g \(\chi_{5472}(2737, \cdot)\) 5472.2.g.a 2 1
5472.2.g.b 16
5472.2.g.c 18
5472.2.g.d 18
5472.2.g.e 36
5472.2.j \(\chi_{5472}(4751, \cdot)\) 5472.2.j.a 4 1
5472.2.j.b 4
5472.2.j.c 28
5472.2.j.d 36
5472.2.k \(\chi_{5472}(2431, \cdot)\) 5472.2.k.a 20 1
5472.2.k.b 20
5472.2.k.c 20
5472.2.k.d 40
5472.2.p \(\chi_{5472}(3761, \cdot)\) 5472.2.p.a 80 1
5472.2.q \(\chi_{5472}(1825, \cdot)\) n/a 432 2
5472.2.r \(\chi_{5472}(2401, \cdot)\) n/a 480 2
5472.2.s \(\chi_{5472}(577, \cdot)\) n/a 200 2
5472.2.t \(\chi_{5472}(961, \cdot)\) n/a 480 2
5472.2.u \(\chi_{5472}(2393, \cdot)\) None 0 2
5472.2.x \(\chi_{5472}(1369, \cdot)\) None 0 2
5472.2.y \(\chi_{5472}(647, \cdot)\) None 0 2
5472.2.bb \(\chi_{5472}(1063, \cdot)\) None 0 2
5472.2.be \(\chi_{5472}(1489, \cdot)\) n/a 472 2
5472.2.bf \(\chi_{5472}(65, \cdot)\) n/a 480 2
5472.2.bg \(\chi_{5472}(2383, \cdot)\) n/a 472 2
5472.2.bh \(\chi_{5472}(4415, \cdot)\) n/a 480 2
5472.2.bm \(\chi_{5472}(1855, \cdot)\) n/a 200 2
5472.2.bn \(\chi_{5472}(3887, \cdot)\) n/a 160 2
5472.2.bq \(\chi_{5472}(113, \cdot)\) n/a 472 2
5472.2.bt \(\chi_{5472}(977, \cdot)\) n/a 472 2
5472.2.bu \(\chi_{5472}(1471, \cdot)\) n/a 480 2
5472.2.bv \(\chi_{5472}(239, \cdot)\) n/a 472 2
5472.2.by \(\chi_{5472}(1103, \cdot)\) n/a 432 2
5472.2.bz \(\chi_{5472}(607, \cdot)\) n/a 480 2
5472.2.cc \(\chi_{5472}(3185, \cdot)\) n/a 160 2
5472.2.cf \(\chi_{5472}(559, \cdot)\) n/a 196 2
5472.2.cg \(\chi_{5472}(1151, \cdot)\) n/a 160 2
5472.2.cj \(\chi_{5472}(49, \cdot)\) n/a 472 2
5472.2.ck \(\chi_{5472}(3713, \cdot)\) n/a 480 2
5472.2.cn \(\chi_{5472}(2849, \cdot)\) n/a 480 2
5472.2.co \(\chi_{5472}(913, \cdot)\) n/a 432 2
5472.2.ct \(\chi_{5472}(191, \cdot)\) n/a 432 2
5472.2.cu \(\chi_{5472}(1519, \cdot)\) n/a 472 2
5472.2.cx \(\chi_{5472}(943, \cdot)\) n/a 472 2
5472.2.cy \(\chi_{5472}(767, \cdot)\) n/a 480 2
5472.2.db \(\chi_{5472}(1873, \cdot)\) n/a 196 2
5472.2.dc \(\chi_{5472}(449, \cdot)\) n/a 160 2
5472.2.dd \(\chi_{5472}(2801, \cdot)\) n/a 472 2
5472.2.di \(\chi_{5472}(31, \cdot)\) n/a 480 2
5472.2.dj \(\chi_{5472}(1679, \cdot)\) n/a 472 2
5472.2.dm \(\chi_{5472}(685, \cdot)\) n/a 1440 4
5472.2.dn \(\chi_{5472}(379, \cdot)\) n/a 1592 4
5472.2.do \(\chi_{5472}(1331, \cdot)\) n/a 1152 4
5472.2.dp \(\chi_{5472}(341, \cdot)\) n/a 1280 4
5472.2.ds \(\chi_{5472}(289, \cdot)\) n/a 600 6
5472.2.dt \(\chi_{5472}(2113, \cdot)\) n/a 1440 6
5472.2.du \(\chi_{5472}(385, \cdot)\) n/a 1440 6
5472.2.dw \(\chi_{5472}(505, \cdot)\) None 0 4
5472.2.dx \(\chi_{5472}(521, \cdot)\) None 0 4
5472.2.ea \(\chi_{5472}(1559, \cdot)\) None 0 4
5472.2.eb \(\chi_{5472}(1015, \cdot)\) None 0 4
5472.2.ed \(\chi_{5472}(103, \cdot)\) None 0 4
5472.2.eg \(\chi_{5472}(1607, \cdot)\) None 0 4
5472.2.ei \(\chi_{5472}(311, \cdot)\) None 0 4
5472.2.ej \(\chi_{5472}(151, \cdot)\) None 0 4
5472.2.em \(\chi_{5472}(569, \cdot)\) None 0 4
5472.2.en \(\chi_{5472}(1033, \cdot)\) None 0 4
5472.2.ep \(\chi_{5472}(121, \cdot)\) None 0 4
5472.2.es \(\chi_{5472}(905, \cdot)\) None 0 4
5472.2.eu \(\chi_{5472}(2345, \cdot)\) None 0 4
5472.2.ev \(\chi_{5472}(457, \cdot)\) None 0 4
5472.2.ey \(\chi_{5472}(487, \cdot)\) None 0 4
5472.2.ez \(\chi_{5472}(1223, \cdot)\) None 0 4
5472.2.fc \(\chi_{5472}(79, \cdot)\) n/a 1416 6
5472.2.fe \(\chi_{5472}(671, \cdot)\) n/a 1440 6
5472.2.ff \(\chi_{5472}(223, \cdot)\) n/a 1440 6
5472.2.fh \(\chi_{5472}(1391, \cdot)\) n/a 1416 6
5472.2.fj \(\chi_{5472}(1409, \cdot)\) n/a 1440 6
5472.2.fl \(\chi_{5472}(625, \cdot)\) n/a 1416 6
5472.2.fp \(\chi_{5472}(1169, \cdot)\) n/a 480 6
5472.2.fq \(\chi_{5472}(1297, \cdot)\) n/a 588 6
5472.2.fs \(\chi_{5472}(737, \cdot)\) n/a 480 6
5472.2.fv \(\chi_{5472}(401, \cdot)\) n/a 1416 6
5472.2.fx \(\chi_{5472}(47, \cdot)\) n/a 1416 6
5472.2.fz \(\chi_{5472}(895, \cdot)\) n/a 1440 6
5472.2.gc \(\chi_{5472}(1135, \cdot)\) n/a 588 6
5472.2.ge \(\chi_{5472}(575, \cdot)\) n/a 480 6
5472.2.gf \(\chi_{5472}(127, \cdot)\) n/a 600 6
5472.2.gh \(\chi_{5472}(719, \cdot)\) n/a 480 6
5472.2.gk \(\chi_{5472}(479, \cdot)\) n/a 1440 6
5472.2.gm \(\chi_{5472}(1231, \cdot)\) n/a 1416 6
5472.2.gp \(\chi_{5472}(497, \cdot)\) n/a 1416 6
5472.2.gq \(\chi_{5472}(529, \cdot)\) n/a 1416 6
5472.2.gs \(\chi_{5472}(257, \cdot)\) n/a 1440 6
5472.2.gu \(\chi_{5472}(835, \cdot)\) n/a 7648 8
5472.2.gv \(\chi_{5472}(229, \cdot)\) n/a 6912 8
5472.2.gy \(\chi_{5472}(1133, \cdot)\) n/a 2560 8
5472.2.gz \(\chi_{5472}(467, \cdot)\) n/a 2560 8
5472.2.he \(\chi_{5472}(11, \cdot)\) n/a 7648 8
5472.2.hf \(\chi_{5472}(293, \cdot)\) n/a 7648 8
5472.2.hg \(\chi_{5472}(83, \cdot)\) n/a 7648 8
5472.2.hh \(\chi_{5472}(221, \cdot)\) n/a 7648 8
5472.2.hm \(\chi_{5472}(277, \cdot)\) n/a 7648 8
5472.2.hn \(\chi_{5472}(259, \cdot)\) n/a 7648 8
5472.2.ho \(\chi_{5472}(349, \cdot)\) n/a 7648 8
5472.2.hp \(\chi_{5472}(331, \cdot)\) n/a 7648 8
5472.2.hu \(\chi_{5472}(1171, \cdot)\) n/a 3184 8
5472.2.hv \(\chi_{5472}(1189, \cdot)\) n/a 3184 8
5472.2.hy \(\chi_{5472}(797, \cdot)\) n/a 7648 8
5472.2.hz \(\chi_{5472}(419, \cdot)\) n/a 6912 8
5472.2.ia \(\chi_{5472}(169, \cdot)\) None 0 12
5472.2.ic \(\chi_{5472}(857, \cdot)\) None 0 12
5472.2.ie \(\chi_{5472}(1031, \cdot)\) None 0 12
5472.2.ih \(\chi_{5472}(775, \cdot)\) None 0 12
5472.2.ij \(\chi_{5472}(215, \cdot)\) None 0 12
5472.2.ik \(\chi_{5472}(295, \cdot)\) None 0 12
5472.2.in \(\chi_{5472}(41, \cdot)\) None 0 12
5472.2.io \(\chi_{5472}(73, \cdot)\) None 0 12
5472.2.iq \(\chi_{5472}(89, \cdot)\) None 0 12
5472.2.it \(\chi_{5472}(25, \cdot)\) None 0 12
5472.2.iv \(\chi_{5472}(439, \cdot)\) None 0 12
5472.2.ix \(\chi_{5472}(23, \cdot)\) None 0 12
5472.2.iz \(\chi_{5472}(131, \cdot)\) n/a 22944 24
5472.2.ja \(\chi_{5472}(29, \cdot)\) n/a 22944 24
5472.2.jd \(\chi_{5472}(85, \cdot)\) n/a 22944 24
5472.2.je \(\chi_{5472}(67, \cdot)\) n/a 22944 24
5472.2.jh \(\chi_{5472}(253, \cdot)\) n/a 9552 24
5472.2.ji \(\chi_{5472}(91, \cdot)\) n/a 9552 24
5472.2.jk \(\chi_{5472}(173, \cdot)\) n/a 22944 24
5472.2.jn \(\chi_{5472}(275, \cdot)\) n/a 22944 24
5472.2.jo \(\chi_{5472}(53, \cdot)\) n/a 7680 24
5472.2.jr \(\chi_{5472}(35, \cdot)\) n/a 7680 24
5472.2.js \(\chi_{5472}(211, \cdot)\) n/a 22944 24
5472.2.jv \(\chi_{5472}(61, \cdot)\) n/a 22944 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5472)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1824))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2736))\)\(^{\oplus 2}\)