Properties

Label 6048.2
Level 6048
Weight 2
Dimension 422336
Nonzero newspaces 96
Sturm bound 3981312

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Defining parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(3981312\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6048))\).

Total New Old
Modular forms 1006848 425536 581312
Cusp forms 983809 422336 561473
Eisenstein series 23039 3200 19839

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6048))\)

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
6048.2.a \(\chi_{6048}(1, \cdot)\) 6048.2.a.a 1 1
6048.2.a.b 1
6048.2.a.c 1
6048.2.a.d 1
6048.2.a.e 1
6048.2.a.f 1
6048.2.a.g 1
6048.2.a.h 1
6048.2.a.i 1
6048.2.a.j 1
6048.2.a.k 1
6048.2.a.l 1
6048.2.a.m 1
6048.2.a.n 1
6048.2.a.o 1
6048.2.a.p 1
6048.2.a.q 1
6048.2.a.r 1
6048.2.a.s 1
6048.2.a.t 1
6048.2.a.u 1
6048.2.a.v 1
6048.2.a.w 1
6048.2.a.x 1
6048.2.a.y 2
6048.2.a.z 2
6048.2.a.ba 2
6048.2.a.bb 2
6048.2.a.bc 2
6048.2.a.bd 2
6048.2.a.be 2
6048.2.a.bf 2
6048.2.a.bg 2
6048.2.a.bh 2
6048.2.a.bi 2
6048.2.a.bj 2
6048.2.a.bk 4
6048.2.a.bl 4
6048.2.a.bm 4
6048.2.a.bn 4
6048.2.a.bo 4
6048.2.a.bp 4
6048.2.a.bq 4
6048.2.a.br 4
6048.2.a.bs 4
6048.2.a.bt 4
6048.2.a.bu 4
6048.2.a.bv 4
6048.2.b \(\chi_{6048}(1567, \cdot)\) n/a 128 1
6048.2.c \(\chi_{6048}(3025, \cdot)\) 6048.2.c.a 2 1
6048.2.c.b 2
6048.2.c.c 8
6048.2.c.d 16
6048.2.c.e 20
6048.2.c.f 24
6048.2.c.g 24
6048.2.h \(\chi_{6048}(2591, \cdot)\) 6048.2.h.a 8 1
6048.2.h.b 8
6048.2.h.c 8
6048.2.h.d 8
6048.2.h.e 8
6048.2.h.f 8
6048.2.h.g 8
6048.2.h.h 16
6048.2.h.i 24
6048.2.i \(\chi_{6048}(4913, \cdot)\) n/a 128 1
6048.2.j \(\chi_{6048}(5615, \cdot)\) 6048.2.j.a 8 1
6048.2.j.b 8
6048.2.j.c 32
6048.2.j.d 48
6048.2.k \(\chi_{6048}(1889, \cdot)\) n/a 128 1
6048.2.p \(\chi_{6048}(4591, \cdot)\) n/a 128 1
6048.2.q \(\chi_{6048}(2305, \cdot)\) n/a 192 2
6048.2.r \(\chi_{6048}(2017, \cdot)\) n/a 144 2
6048.2.s \(\chi_{6048}(865, \cdot)\) n/a 256 2
6048.2.t \(\chi_{6048}(289, \cdot)\) n/a 192 2
6048.2.v \(\chi_{6048}(1079, \cdot)\) None 0 2
6048.2.x \(\chi_{6048}(55, \cdot)\) None 0 2
6048.2.z \(\chi_{6048}(1513, \cdot)\) None 0 2
6048.2.bb \(\chi_{6048}(377, \cdot)\) None 0 2
6048.2.be \(\chi_{6048}(1873, \cdot)\) n/a 184 2
6048.2.bf \(\chi_{6048}(4735, \cdot)\) n/a 192 2
6048.2.bg \(\chi_{6048}(17, \cdot)\) n/a 184 2
6048.2.bh \(\chi_{6048}(4895, \cdot)\) n/a 192 2
6048.2.bm \(\chi_{6048}(559, \cdot)\) n/a 184 2
6048.2.bn \(\chi_{6048}(4303, \cdot)\) n/a 184 2
6048.2.bs \(\chi_{6048}(271, \cdot)\) n/a 256 2
6048.2.bt \(\chi_{6048}(1025, \cdot)\) n/a 256 2
6048.2.bu \(\chi_{6048}(431, \cdot)\) n/a 256 2
6048.2.bz \(\chi_{6048}(1583, \cdot)\) n/a 144 2
6048.2.ca \(\chi_{6048}(5057, \cdot)\) n/a 192 2
6048.2.cb \(\chi_{6048}(4463, \cdot)\) n/a 184 2
6048.2.cc \(\chi_{6048}(3905, \cdot)\) n/a 192 2
6048.2.ch \(\chi_{6048}(575, \cdot)\) n/a 144 2
6048.2.ci \(\chi_{6048}(2033, \cdot)\) n/a 184 2
6048.2.cj \(\chi_{6048}(1439, \cdot)\) n/a 192 2
6048.2.ck \(\chi_{6048}(881, \cdot)\) n/a 184 2
6048.2.cp \(\chi_{6048}(593, \cdot)\) n/a 256 2
6048.2.cq \(\chi_{6048}(863, \cdot)\) n/a 256 2
6048.2.cr \(\chi_{6048}(1297, \cdot)\) n/a 256 2
6048.2.cs \(\chi_{6048}(703, \cdot)\) n/a 256 2
6048.2.cx \(\chi_{6048}(3583, \cdot)\) n/a 192 2
6048.2.cy \(\chi_{6048}(5329, \cdot)\) n/a 184 2
6048.2.cz \(\chi_{6048}(1279, \cdot)\) n/a 192 2
6048.2.da \(\chi_{6048}(1009, \cdot)\) n/a 144 2
6048.2.df \(\chi_{6048}(1601, \cdot)\) n/a 192 2
6048.2.dg \(\chi_{6048}(1871, \cdot)\) n/a 184 2
6048.2.dh \(\chi_{6048}(1711, \cdot)\) n/a 184 2
6048.2.dk \(\chi_{6048}(1133, \cdot)\) n/a 2048 4
6048.2.dm \(\chi_{6048}(757, \cdot)\) n/a 1536 4
6048.2.do \(\chi_{6048}(323, \cdot)\) n/a 1536 4
6048.2.dq \(\chi_{6048}(811, \cdot)\) n/a 2048 4
6048.2.ds \(\chi_{6048}(673, \cdot)\) n/a 1296 6
6048.2.dt \(\chi_{6048}(193, \cdot)\) n/a 1728 6
6048.2.du \(\chi_{6048}(1537, \cdot)\) n/a 1728 6
6048.2.dv \(\chi_{6048}(1063, \cdot)\) None 0 4
6048.2.dx \(\chi_{6048}(71, \cdot)\) None 0 4
6048.2.dz \(\chi_{6048}(361, \cdot)\) None 0 4
6048.2.ec \(\chi_{6048}(521, \cdot)\) None 0 4
6048.2.ed \(\chi_{6048}(2105, \cdot)\) None 0 4
6048.2.ef \(\chi_{6048}(2377, \cdot)\) None 0 4
6048.2.ei \(\chi_{6048}(793, \cdot)\) None 0 4
6048.2.ej \(\chi_{6048}(89, \cdot)\) None 0 4
6048.2.el \(\chi_{6048}(359, \cdot)\) None 0 4
6048.2.en \(\chi_{6048}(1783, \cdot)\) None 0 4
6048.2.eq \(\chi_{6048}(1207, \cdot)\) None 0 4
6048.2.es \(\chi_{6048}(1367, \cdot)\) None 0 4
6048.2.et \(\chi_{6048}(1943, \cdot)\) None 0 4
6048.2.ev \(\chi_{6048}(199, \cdot)\) None 0 4
6048.2.ex \(\chi_{6048}(1385, \cdot)\) None 0 4
6048.2.ez \(\chi_{6048}(505, \cdot)\) None 0 4
6048.2.fc \(\chi_{6048}(767, \cdot)\) n/a 1728 6
6048.2.fe \(\chi_{6048}(367, \cdot)\) n/a 1704 6
6048.2.ff \(\chi_{6048}(607, \cdot)\) n/a 1728 6
6048.2.fh \(\chi_{6048}(527, \cdot)\) n/a 1704 6
6048.2.fj \(\chi_{6048}(689, \cdot)\) n/a 1704 6
6048.2.fn \(\chi_{6048}(209, \cdot)\) n/a 1704 6
6048.2.fq \(\chi_{6048}(1201, \cdot)\) n/a 1704 6
6048.2.fr \(\chi_{6048}(545, \cdot)\) n/a 1728 6
6048.2.ft \(\chi_{6048}(337, \cdot)\) n/a 1296 6
6048.2.fw \(\chi_{6048}(929, \cdot)\) n/a 1728 6
6048.2.fx \(\chi_{6048}(1103, \cdot)\) n/a 1704 6
6048.2.ga \(\chi_{6048}(223, \cdot)\) n/a 1728 6
6048.2.gc \(\chi_{6048}(239, \cdot)\) n/a 1296 6
6048.2.gd \(\chi_{6048}(31, \cdot)\) n/a 1728 6
6048.2.gg \(\chi_{6048}(943, \cdot)\) n/a 1704 6
6048.2.gh \(\chi_{6048}(1247, \cdot)\) n/a 1296 6
6048.2.gj \(\chi_{6048}(1231, \cdot)\) n/a 1704 6
6048.2.gm \(\chi_{6048}(95, \cdot)\) n/a 1728 6
6048.2.go \(\chi_{6048}(257, \cdot)\) n/a 1728 6
6048.2.gq \(\chi_{6048}(529, \cdot)\) n/a 1704 6
6048.2.gs \(\chi_{6048}(1265, \cdot)\) n/a 1704 6
6048.2.gv \(\chi_{6048}(253, \cdot)\) n/a 2304 8
6048.2.gx \(\chi_{6048}(125, \cdot)\) n/a 3040 8
6048.2.gy \(\chi_{6048}(611, \cdot)\) n/a 3040 8
6048.2.hc \(\chi_{6048}(1027, \cdot)\) n/a 4096 8
6048.2.hd \(\chi_{6048}(19, \cdot)\) n/a 3040 8
6048.2.hg \(\chi_{6048}(179, \cdot)\) n/a 3040 8
6048.2.hh \(\chi_{6048}(107, \cdot)\) n/a 4096 8
6048.2.hi \(\chi_{6048}(451, \cdot)\) n/a 3040 8
6048.2.hk \(\chi_{6048}(341, \cdot)\) n/a 3040 8
6048.2.ho \(\chi_{6048}(1045, \cdot)\) n/a 3040 8
6048.2.hp \(\chi_{6048}(109, \cdot)\) n/a 4096 8
6048.2.hs \(\chi_{6048}(269, \cdot)\) n/a 4096 8
6048.2.ht \(\chi_{6048}(773, \cdot)\) n/a 3040 8
6048.2.hu \(\chi_{6048}(37, \cdot)\) n/a 3040 8
6048.2.hx \(\chi_{6048}(307, \cdot)\) n/a 3040 8
6048.2.hz \(\chi_{6048}(827, \cdot)\) n/a 2304 8
6048.2.ia \(\chi_{6048}(103, \cdot)\) None 0 12
6048.2.id \(\chi_{6048}(23, \cdot)\) None 0 12
6048.2.ie \(\chi_{6048}(457, \cdot)\) None 0 12
6048.2.ig \(\chi_{6048}(169, \cdot)\) None 0 12
6048.2.ij \(\chi_{6048}(41, \cdot)\) None 0 12
6048.2.il \(\chi_{6048}(185, \cdot)\) None 0 12
6048.2.in \(\chi_{6048}(391, \cdot)\) None 0 12
6048.2.ip \(\chi_{6048}(439, \cdot)\) None 0 12
6048.2.iq \(\chi_{6048}(599, \cdot)\) None 0 12
6048.2.is \(\chi_{6048}(407, \cdot)\) None 0 12
6048.2.iv \(\chi_{6048}(25, \cdot)\) None 0 12
6048.2.iw \(\chi_{6048}(761, \cdot)\) None 0 12
6048.2.iy \(\chi_{6048}(5, \cdot)\) n/a 27552 24
6048.2.iz \(\chi_{6048}(277, \cdot)\) n/a 27552 24
6048.2.jg \(\chi_{6048}(347, \cdot)\) n/a 27552 24
6048.2.jh \(\chi_{6048}(187, \cdot)\) n/a 27552 24
6048.2.ji \(\chi_{6048}(139, \cdot)\) n/a 27552 24
6048.2.jj \(\chi_{6048}(155, \cdot)\) n/a 20736 24
6048.2.jk \(\chi_{6048}(205, \cdot)\) n/a 27552 24
6048.2.jl \(\chi_{6048}(173, \cdot)\) n/a 27552 24
6048.2.jm \(\chi_{6048}(293, \cdot)\) n/a 27552 24
6048.2.jn \(\chi_{6048}(85, \cdot)\) n/a 20736 24
6048.2.ju \(\chi_{6048}(115, \cdot)\) n/a 27552 24
6048.2.jv \(\chi_{6048}(11, \cdot)\) n/a 27552 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6048))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6048)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1512))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2016))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3024))\)\(^{\oplus 2}\)