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Properties

Label 4752.2
Level 4752
Weight 2
Dimension 270576
Nonzero newspaces 48
Sturm bound 2488320

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Defining parameters

Level: \( N \) = \( 4752 = 2^{4} \cdot 3^{3} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2488320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4752))\).

Total New Old
Modular forms 630480 273168 357312
Cusp forms 613681 270576 343105
Eisenstein series 16799 2592 14207

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4752))\)

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
4752.2.a \(\chi_{4752}(1, \cdot)\) 4752.2.a.a 1 1
4752.2.a.b 1
4752.2.a.c 1
4752.2.a.d 1
4752.2.a.e 1
4752.2.a.f 1
4752.2.a.g 1
4752.2.a.h 1
4752.2.a.i 1
4752.2.a.j 1
4752.2.a.k 1
4752.2.a.l 1
4752.2.a.m 1
4752.2.a.n 1
4752.2.a.o 1
4752.2.a.p 1
4752.2.a.q 1
4752.2.a.r 1
4752.2.a.s 1
4752.2.a.t 1
4752.2.a.u 2
4752.2.a.v 2
4752.2.a.w 2
4752.2.a.x 2
4752.2.a.y 2
4752.2.a.z 2
4752.2.a.ba 2
4752.2.a.bb 2
4752.2.a.bc 2
4752.2.a.bd 2
4752.2.a.be 2
4752.2.a.bf 2
4752.2.a.bg 3
4752.2.a.bh 3
4752.2.a.bi 3
4752.2.a.bj 3
4752.2.a.bk 3
4752.2.a.bl 3
4752.2.a.bm 3
4752.2.a.bn 3
4752.2.a.bo 3
4752.2.a.bp 3
4752.2.a.bq 3
4752.2.a.br 3
4752.2.b \(\chi_{4752}(593, \cdot)\) 4752.2.b.a 4 1
4752.2.b.b 4
4752.2.b.c 4
4752.2.b.d 4
4752.2.b.e 8
4752.2.b.f 8
4752.2.b.g 8
4752.2.b.h 8
4752.2.b.i 12
4752.2.b.j 12
4752.2.b.k 12
4752.2.b.l 12
4752.2.d \(\chi_{4752}(3455, \cdot)\) 4752.2.d.a 2 1
4752.2.d.b 2
4752.2.d.c 2
4752.2.d.d 2
4752.2.d.e 4
4752.2.d.f 4
4752.2.d.g 6
4752.2.d.h 6
4752.2.d.i 6
4752.2.d.j 6
4752.2.d.k 8
4752.2.d.l 8
4752.2.d.m 12
4752.2.d.n 12
4752.2.f \(\chi_{4752}(2377, \cdot)\) None 0 1
4752.2.h \(\chi_{4752}(3079, \cdot)\) None 0 1
4752.2.k \(\chi_{4752}(1079, \cdot)\) None 0 1
4752.2.m \(\chi_{4752}(2969, \cdot)\) None 0 1
4752.2.o \(\chi_{4752}(703, \cdot)\) 4752.2.o.a 4 1
4752.2.o.b 4
4752.2.o.c 8
4752.2.o.d 16
4752.2.o.e 32
4752.2.o.f 32
4752.2.q \(\chi_{4752}(1585, \cdot)\) n/a 120 2
4752.2.r \(\chi_{4752}(1891, \cdot)\) n/a 768 2
4752.2.u \(\chi_{4752}(1189, \cdot)\) n/a 640 2
4752.2.v \(\chi_{4752}(2267, \cdot)\) n/a 640 2
4752.2.y \(\chi_{4752}(1781, \cdot)\) n/a 768 2
4752.2.z \(\chi_{4752}(433, \cdot)\) n/a 384 4
4752.2.bc \(\chi_{4752}(2287, \cdot)\) n/a 144 2
4752.2.be \(\chi_{4752}(1385, \cdot)\) None 0 2
4752.2.bg \(\chi_{4752}(2663, \cdot)\) None 0 2
4752.2.bh \(\chi_{4752}(1495, \cdot)\) None 0 2
4752.2.bj \(\chi_{4752}(793, \cdot)\) None 0 2
4752.2.bl \(\chi_{4752}(287, \cdot)\) n/a 120 2
4752.2.bn \(\chi_{4752}(2177, \cdot)\) n/a 140 2
4752.2.bp \(\chi_{4752}(529, \cdot)\) n/a 1080 6
4752.2.br \(\chi_{4752}(271, \cdot)\) n/a 384 4
4752.2.bt \(\chi_{4752}(809, \cdot)\) None 0 4
4752.2.bv \(\chi_{4752}(647, \cdot)\) None 0 4
4752.2.by \(\chi_{4752}(919, \cdot)\) None 0 4
4752.2.ca \(\chi_{4752}(1081, \cdot)\) None 0 4
4752.2.cc \(\chi_{4752}(863, \cdot)\) n/a 384 4
4752.2.ce \(\chi_{4752}(161, \cdot)\) n/a 384 4
4752.2.cg \(\chi_{4752}(683, \cdot)\) n/a 960 4
4752.2.ch \(\chi_{4752}(197, \cdot)\) n/a 1136 4
4752.2.ck \(\chi_{4752}(307, \cdot)\) n/a 1136 4
4752.2.cl \(\chi_{4752}(397, \cdot)\) n/a 960 4
4752.2.cn \(\chi_{4752}(289, \cdot)\) n/a 560 8
4752.2.cq \(\chi_{4752}(329, \cdot)\) None 0 6
4752.2.cr \(\chi_{4752}(65, \cdot)\) n/a 1284 6
4752.2.cu \(\chi_{4752}(265, \cdot)\) None 0 6
4752.2.cv \(\chi_{4752}(175, \cdot)\) n/a 1296 6
4752.2.cy \(\chi_{4752}(23, \cdot)\) None 0 6
4752.2.cz \(\chi_{4752}(815, \cdot)\) n/a 1080 6
4752.2.dc \(\chi_{4752}(439, \cdot)\) None 0 6
4752.2.dd \(\chi_{4752}(701, \cdot)\) n/a 3072 8
4752.2.dg \(\chi_{4752}(323, \cdot)\) n/a 3072 8
4752.2.dh \(\chi_{4752}(757, \cdot)\) n/a 3072 8
4752.2.dk \(\chi_{4752}(811, \cdot)\) n/a 3072 8
4752.2.dm \(\chi_{4752}(17, \cdot)\) n/a 560 8
4752.2.do \(\chi_{4752}(575, \cdot)\) n/a 576 8
4752.2.dq \(\chi_{4752}(361, \cdot)\) None 0 8
4752.2.ds \(\chi_{4752}(343, \cdot)\) None 0 8
4752.2.dt \(\chi_{4752}(71, \cdot)\) None 0 8
4752.2.dv \(\chi_{4752}(233, \cdot)\) None 0 8
4752.2.dx \(\chi_{4752}(127, \cdot)\) n/a 576 8
4752.2.ea \(\chi_{4752}(461, \cdot)\) n/a 10320 12
4752.2.ed \(\chi_{4752}(133, \cdot)\) n/a 8640 12
4752.2.ee \(\chi_{4752}(43, \cdot)\) n/a 10320 12
4752.2.eh \(\chi_{4752}(155, \cdot)\) n/a 8640 12
4752.2.ei \(\chi_{4752}(49, \cdot)\) n/a 5136 24
4752.2.ek \(\chi_{4752}(37, \cdot)\) n/a 4544 16
4752.2.el \(\chi_{4752}(19, \cdot)\) n/a 4544 16
4752.2.eo \(\chi_{4752}(413, \cdot)\) n/a 4544 16
4752.2.ep \(\chi_{4752}(179, \cdot)\) n/a 4544 16
4752.2.er \(\chi_{4752}(7, \cdot)\) None 0 24
4752.2.eu \(\chi_{4752}(47, \cdot)\) n/a 5184 24
4752.2.ev \(\chi_{4752}(119, \cdot)\) None 0 24
4752.2.ey \(\chi_{4752}(79, \cdot)\) n/a 5184 24
4752.2.ez \(\chi_{4752}(25, \cdot)\) None 0 24
4752.2.fc \(\chi_{4752}(497, \cdot)\) n/a 5136 24
4752.2.fd \(\chi_{4752}(41, \cdot)\) None 0 24
4752.2.fg \(\chi_{4752}(59, \cdot)\) n/a 41280 48
4752.2.fj \(\chi_{4752}(139, \cdot)\) n/a 41280 48
4752.2.fk \(\chi_{4752}(157, \cdot)\) n/a 41280 48
4752.2.fn \(\chi_{4752}(29, \cdot)\) n/a 41280 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2376))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4752))\)\(^{\oplus 1}\)