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Properties

Label 4620.2
Level 4620
Weight 2
Dimension 207904
Nonzero newspaces 96
Sturm bound 2211840

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Defining parameters

Level: \( N \) = \( 4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(2211840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4620))\).

Total New Old
Modular forms 562560 210048 352512
Cusp forms 543361 207904 335457
Eisenstein series 19199 2144 17055

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4620))\)

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
4620.2.a \(\chi_{4620}(1, \cdot)\) 4620.2.a.a 1 1
4620.2.a.b 1
4620.2.a.c 1
4620.2.a.d 1
4620.2.a.e 1
4620.2.a.f 1
4620.2.a.g 1
4620.2.a.h 1
4620.2.a.i 1
4620.2.a.j 1
4620.2.a.k 1
4620.2.a.l 1
4620.2.a.m 1
4620.2.a.n 1
4620.2.a.o 2
4620.2.a.p 2
4620.2.a.q 2
4620.2.a.r 2
4620.2.a.s 2
4620.2.a.t 3
4620.2.a.u 3
4620.2.a.v 3
4620.2.a.w 3
4620.2.a.x 4
4620.2.f \(\chi_{4620}(769, \cdot)\) 4620.2.f.a 4 1
4620.2.f.b 4
4620.2.f.c 4
4620.2.f.d 4
4620.2.f.e 40
4620.2.f.f 40
4620.2.g \(\chi_{4620}(1891, \cdot)\) n/a 288 1
4620.2.h \(\chi_{4620}(1849, \cdot)\) 4620.2.h.a 2 1
4620.2.h.b 2
4620.2.h.c 2
4620.2.h.d 14
4620.2.h.e 14
4620.2.h.f 14
4620.2.h.g 16
4620.2.i \(\chi_{4620}(1651, \cdot)\) n/a 320 1
4620.2.j \(\chi_{4620}(1079, \cdot)\) n/a 720 1
4620.2.k \(\chi_{4620}(881, \cdot)\) n/a 104 1
4620.2.l \(\chi_{4620}(4619, \cdot)\) n/a 1136 1
4620.2.m \(\chi_{4620}(1121, \cdot)\) 4620.2.m.a 48 1
4620.2.m.b 48
4620.2.r \(\chi_{4620}(2729, \cdot)\) n/a 160 1
4620.2.s \(\chi_{4620}(3851, \cdot)\) n/a 480 1
4620.2.t \(\chi_{4620}(2969, \cdot)\) n/a 144 1
4620.2.u \(\chi_{4620}(2771, \cdot)\) n/a 768 1
4620.2.bd \(\chi_{4620}(3739, \cdot)\) n/a 432 1
4620.2.be \(\chi_{4620}(3541, \cdot)\) 4620.2.be.a 4 1
4620.2.be.b 4
4620.2.be.c 12
4620.2.be.d 12
4620.2.be.e 32
4620.2.bf \(\chi_{4620}(3499, \cdot)\) n/a 480 1
4620.2.bg \(\chi_{4620}(2641, \cdot)\) n/a 104 2
4620.2.bh \(\chi_{4620}(3233, \cdot)\) n/a 384 2
4620.2.bi \(\chi_{4620}(1583, \cdot)\) n/a 1728 2
4620.2.bn \(\chi_{4620}(617, \cdot)\) n/a 240 2
4620.2.bo \(\chi_{4620}(1343, \cdot)\) n/a 1920 2
4620.2.bp \(\chi_{4620}(2113, \cdot)\) n/a 160 2
4620.2.bq \(\chi_{4620}(463, \cdot)\) n/a 720 2
4620.2.bv \(\chi_{4620}(2353, \cdot)\) n/a 144 2
4620.2.bw \(\chi_{4620}(307, \cdot)\) n/a 1152 2
4620.2.bx \(\chi_{4620}(421, \cdot)\) n/a 192 4
4620.2.cc \(\chi_{4620}(2201, \cdot)\) n/a 216 2
4620.2.cd \(\chi_{4620}(3719, \cdot)\) n/a 1920 2
4620.2.ce \(\chi_{4620}(3761, \cdot)\) n/a 256 2
4620.2.cf \(\chi_{4620}(1319, \cdot)\) n/a 2272 2
4620.2.cg \(\chi_{4620}(571, \cdot)\) n/a 768 2
4620.2.ch \(\chi_{4620}(2089, \cdot)\) n/a 192 2
4620.2.ci \(\chi_{4620}(2971, \cdot)\) n/a 640 2
4620.2.cj \(\chi_{4620}(529, \cdot)\) n/a 160 2
4620.2.co \(\chi_{4620}(241, \cdot)\) n/a 128 2
4620.2.cp \(\chi_{4620}(1759, \cdot)\) n/a 1152 2
4620.2.cq \(\chi_{4620}(199, \cdot)\) n/a 960 2
4620.2.cz \(\chi_{4620}(1871, \cdot)\) n/a 1280 2
4620.2.da \(\chi_{4620}(89, \cdot)\) n/a 320 2
4620.2.db \(\chi_{4620}(131, \cdot)\) n/a 1536 2
4620.2.dc \(\chi_{4620}(989, \cdot)\) n/a 384 2
4620.2.dd \(\chi_{4620}(559, \cdot)\) n/a 2304 4
4620.2.de \(\chi_{4620}(601, \cdot)\) n/a 256 4
4620.2.df \(\chi_{4620}(799, \cdot)\) n/a 1728 4
4620.2.do \(\chi_{4620}(1091, \cdot)\) n/a 3072 4
4620.2.dp \(\chi_{4620}(29, \cdot)\) n/a 576 4
4620.2.dq \(\chi_{4620}(71, \cdot)\) n/a 2304 4
4620.2.dr \(\chi_{4620}(1049, \cdot)\) n/a 768 4
4620.2.dw \(\chi_{4620}(281, \cdot)\) n/a 384 4
4620.2.dx \(\chi_{4620}(1679, \cdot)\) n/a 4544 4
4620.2.dy \(\chi_{4620}(1301, \cdot)\) n/a 512 4
4620.2.dz \(\chi_{4620}(1499, \cdot)\) n/a 3456 4
4620.2.ea \(\chi_{4620}(2071, \cdot)\) n/a 1536 4
4620.2.eb \(\chi_{4620}(169, \cdot)\) n/a 288 4
4620.2.ec \(\chi_{4620}(211, \cdot)\) n/a 1152 4
4620.2.ed \(\chi_{4620}(349, \cdot)\) n/a 384 4
4620.2.ek \(\chi_{4620}(397, \cdot)\) n/a 320 4
4620.2.el \(\chi_{4620}(67, \cdot)\) n/a 1920 4
4620.2.em \(\chi_{4620}(373, \cdot)\) n/a 384 4
4620.2.en \(\chi_{4620}(703, \cdot)\) n/a 2304 4
4620.2.es \(\chi_{4620}(593, \cdot)\) n/a 768 4
4620.2.et \(\chi_{4620}(263, \cdot)\) n/a 4544 4
4620.2.eu \(\chi_{4620}(2333, \cdot)\) n/a 640 4
4620.2.ev \(\chi_{4620}(2663, \cdot)\) n/a 3840 4
4620.2.ey \(\chi_{4620}(361, \cdot)\) n/a 512 8
4620.2.ez \(\chi_{4620}(1063, \cdot)\) n/a 4608 8
4620.2.fa \(\chi_{4620}(337, \cdot)\) n/a 576 8
4620.2.ff \(\chi_{4620}(883, \cdot)\) n/a 3456 8
4620.2.fg \(\chi_{4620}(97, \cdot)\) n/a 768 8
4620.2.fh \(\chi_{4620}(587, \cdot)\) n/a 9088 8
4620.2.fi \(\chi_{4620}(113, \cdot)\) n/a 1152 8
4620.2.fn \(\chi_{4620}(743, \cdot)\) n/a 6912 8
4620.2.fo \(\chi_{4620}(293, \cdot)\) n/a 1536 8
4620.2.fp \(\chi_{4620}(149, \cdot)\) n/a 1536 8
4620.2.fq \(\chi_{4620}(1151, \cdot)\) n/a 6144 8
4620.2.fr \(\chi_{4620}(269, \cdot)\) n/a 1536 8
4620.2.fs \(\chi_{4620}(191, \cdot)\) n/a 6144 8
4620.2.gb \(\chi_{4620}(619, \cdot)\) n/a 4608 8
4620.2.gc \(\chi_{4620}(79, \cdot)\) n/a 4608 8
4620.2.gd \(\chi_{4620}(61, \cdot)\) n/a 512 8
4620.2.gi \(\chi_{4620}(289, \cdot)\) n/a 768 8
4620.2.gj \(\chi_{4620}(31, \cdot)\) n/a 3072 8
4620.2.gk \(\chi_{4620}(409, \cdot)\) n/a 768 8
4620.2.gl \(\chi_{4620}(151, \cdot)\) n/a 3072 8
4620.2.gm \(\chi_{4620}(299, \cdot)\) n/a 9088 8
4620.2.gn \(\chi_{4620}(821, \cdot)\) n/a 1024 8
4620.2.go \(\chi_{4620}(179, \cdot)\) n/a 9088 8
4620.2.gp \(\chi_{4620}(521, \cdot)\) n/a 1024 8
4620.2.gw \(\chi_{4620}(47, \cdot)\) n/a 18176 16
4620.2.gx \(\chi_{4620}(53, \cdot)\) n/a 3072 16
4620.2.gy \(\chi_{4620}(107, \cdot)\) n/a 18176 16
4620.2.gz \(\chi_{4620}(17, \cdot)\) n/a 3072 16
4620.2.he \(\chi_{4620}(283, \cdot)\) n/a 9216 16
4620.2.hf \(\chi_{4620}(193, \cdot)\) n/a 1536 16
4620.2.hg \(\chi_{4620}(163, \cdot)\) n/a 9216 16
4620.2.hh \(\chi_{4620}(157, \cdot)\) n/a 1536 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4620))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4620)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2310))\)\(^{\oplus 2}\)