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Properties

Label 4725.2
Level 4725
Weight 2
Dimension 539398
Nonzero newspaces 96
Sturm bound 3110400

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Defining parameters

Level: \( N \) = \( 4725 = 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(3110400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4725))\).

Total New Old
Modular forms 787680 545958 241722
Cusp forms 767521 539398 228123
Eisenstein series 20159 6560 13599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4725))\)

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
4725.2.a \(\chi_{4725}(1, \cdot)\) 4725.2.a.a 1 1
4725.2.a.b 1
4725.2.a.c 1
4725.2.a.d 1
4725.2.a.e 1
4725.2.a.f 1
4725.2.a.g 1
4725.2.a.h 1
4725.2.a.i 1
4725.2.a.j 1
4725.2.a.k 1
4725.2.a.l 1
4725.2.a.m 1
4725.2.a.n 1
4725.2.a.o 1
4725.2.a.p 1
4725.2.a.q 1
4725.2.a.r 1
4725.2.a.s 1
4725.2.a.t 1
4725.2.a.u 2
4725.2.a.v 2
4725.2.a.w 2
4725.2.a.x 2
4725.2.a.y 2
4725.2.a.z 2
4725.2.a.ba 2
4725.2.a.bb 2
4725.2.a.bc 2
4725.2.a.bd 2
4725.2.a.be 2
4725.2.a.bf 2
4725.2.a.bg 2
4725.2.a.bh 2
4725.2.a.bi 3
4725.2.a.bj 3
4725.2.a.bk 3
4725.2.a.bl 3
4725.2.a.bm 4
4725.2.a.bn 4
4725.2.a.bo 4
4725.2.a.bp 4
4725.2.a.bq 4
4725.2.a.br 4
4725.2.a.bs 4
4725.2.a.bt 4
4725.2.a.bu 4
4725.2.a.bv 4
4725.2.a.bw 4
4725.2.a.bx 4
4725.2.a.by 4
4725.2.a.bz 4
4725.2.a.ca 5
4725.2.a.cb 5
4725.2.a.cc 5
4725.2.a.cd 5
4725.2.a.ce 8
4725.2.a.cf 8
4725.2.b \(\chi_{4725}(3401, \cdot)\) n/a 202 1
4725.2.d \(\chi_{4725}(1324, \cdot)\) n/a 144 1
4725.2.g \(\chi_{4725}(4724, \cdot)\) n/a 192 1
4725.2.i \(\chi_{4725}(1576, \cdot)\) n/a 228 2
4725.2.j \(\chi_{4725}(676, \cdot)\) n/a 406 2
4725.2.k \(\chi_{4725}(1801, \cdot)\) n/a 292 2
4725.2.l \(\chi_{4725}(226, \cdot)\) n/a 292 2
4725.2.m \(\chi_{4725}(1268, \cdot)\) n/a 288 2
4725.2.p \(\chi_{4725}(3268, \cdot)\) n/a 384 2
4725.2.q \(\chi_{4725}(946, \cdot)\) n/a 960 4
4725.2.s \(\chi_{4725}(424, \cdot)\) n/a 280 2
4725.2.u \(\chi_{4725}(3176, \cdot)\) n/a 292 2
4725.2.v \(\chi_{4725}(2474, \cdot)\) n/a 280 2
4725.2.ba \(\chi_{4725}(1574, \cdot)\) n/a 280 2
4725.2.bc \(\chi_{4725}(1349, \cdot)\) n/a 384 2
4725.2.bf \(\chi_{4725}(1151, \cdot)\) n/a 292 2
4725.2.bg \(\chi_{4725}(1999, \cdot)\) n/a 384 2
4725.2.bi \(\chi_{4725}(2899, \cdot)\) n/a 216 2
4725.2.bk \(\chi_{4725}(26, \cdot)\) n/a 406 2
4725.2.bm \(\chi_{4725}(251, \cdot)\) n/a 292 2
4725.2.bp \(\chi_{4725}(3124, \cdot)\) n/a 280 2
4725.2.br \(\chi_{4725}(899, \cdot)\) n/a 280 2
4725.2.bt \(\chi_{4725}(1201, \cdot)\) n/a 2700 6
4725.2.bu \(\chi_{4725}(526, \cdot)\) n/a 2052 6
4725.2.bv \(\chi_{4725}(151, \cdot)\) n/a 2700 6
4725.2.bx \(\chi_{4725}(944, \cdot)\) n/a 1280 4
4725.2.ca \(\chi_{4725}(379, \cdot)\) n/a 960 4
4725.2.cc \(\chi_{4725}(566, \cdot)\) n/a 1280 4
4725.2.cd \(\chi_{4725}(1018, \cdot)\) n/a 560 4
4725.2.cg \(\chi_{4725}(3068, \cdot)\) n/a 560 4
4725.2.ci \(\chi_{4725}(368, \cdot)\) n/a 560 4
4725.2.ck \(\chi_{4725}(82, \cdot)\) n/a 768 4
4725.2.cm \(\chi_{4725}(118, \cdot)\) n/a 560 4
4725.2.cn \(\chi_{4725}(2843, \cdot)\) n/a 432 4
4725.2.cp \(\chi_{4725}(107, \cdot)\) n/a 768 4
4725.2.cr \(\chi_{4725}(3043, \cdot)\) n/a 560 4
4725.2.ct \(\chi_{4725}(46, \cdot)\) n/a 1888 8
4725.2.cu \(\chi_{4725}(361, \cdot)\) n/a 1888 8
4725.2.cv \(\chi_{4725}(541, \cdot)\) n/a 2560 8
4725.2.cw \(\chi_{4725}(316, \cdot)\) n/a 1440 8
4725.2.cx \(\chi_{4725}(824, \cdot)\) n/a 2568 6
4725.2.dc \(\chi_{4725}(299, \cdot)\) n/a 2568 6
4725.2.de \(\chi_{4725}(524, \cdot)\) n/a 2568 6
4725.2.dg \(\chi_{4725}(499, \cdot)\) n/a 2568 6
4725.2.dj \(\chi_{4725}(551, \cdot)\) n/a 2700 6
4725.2.dl \(\chi_{4725}(776, \cdot)\) n/a 2700 6
4725.2.dn \(\chi_{4725}(949, \cdot)\) n/a 2568 6
4725.2.dp \(\chi_{4725}(274, \cdot)\) n/a 1944 6
4725.2.dq \(\chi_{4725}(101, \cdot)\) n/a 2700 6
4725.2.ds \(\chi_{4725}(433, \cdot)\) n/a 2560 8
4725.2.dv \(\chi_{4725}(323, \cdot)\) n/a 1920 8
4725.2.dx \(\chi_{4725}(719, \cdot)\) n/a 1888 8
4725.2.dz \(\chi_{4725}(289, \cdot)\) n/a 1888 8
4725.2.ec \(\chi_{4725}(881, \cdot)\) n/a 1888 8
4725.2.ee \(\chi_{4725}(836, \cdot)\) n/a 2560 8
4725.2.eg \(\chi_{4725}(64, \cdot)\) n/a 1440 8
4725.2.ei \(\chi_{4725}(109, \cdot)\) n/a 2560 8
4725.2.ej \(\chi_{4725}(206, \cdot)\) n/a 1888 8
4725.2.em \(\chi_{4725}(269, \cdot)\) n/a 2560 8
4725.2.eo \(\chi_{4725}(314, \cdot)\) n/a 1888 8
4725.2.et \(\chi_{4725}(89, \cdot)\) n/a 1888 8
4725.2.eu \(\chi_{4725}(341, \cdot)\) n/a 1888 8
4725.2.ew \(\chi_{4725}(604, \cdot)\) n/a 1888 8
4725.2.ez \(\chi_{4725}(893, \cdot)\) n/a 5136 12
4725.2.fa \(\chi_{4725}(643, \cdot)\) n/a 5136 12
4725.2.fc \(\chi_{4725}(157, \cdot)\) n/a 5136 12
4725.2.fe \(\chi_{4725}(218, \cdot)\) n/a 3888 12
4725.2.fg \(\chi_{4725}(32, \cdot)\) n/a 5136 12
4725.2.fj \(\chi_{4725}(418, \cdot)\) n/a 5136 12
4725.2.fk \(\chi_{4725}(121, \cdot)\) n/a 17184 24
4725.2.fl \(\chi_{4725}(16, \cdot)\) n/a 17184 24
4725.2.fm \(\chi_{4725}(106, \cdot)\) n/a 12960 24
4725.2.fo \(\chi_{4725}(208, \cdot)\) n/a 3776 16
4725.2.fq \(\chi_{4725}(53, \cdot)\) n/a 5120 16
4725.2.fs \(\chi_{4725}(8, \cdot)\) n/a 2880 16
4725.2.ft \(\chi_{4725}(748, \cdot)\) n/a 3776 16
4725.2.fv \(\chi_{4725}(703, \cdot)\) n/a 5120 16
4725.2.fx \(\chi_{4725}(548, \cdot)\) n/a 3776 16
4725.2.fz \(\chi_{4725}(233, \cdot)\) n/a 3776 16
4725.2.gc \(\chi_{4725}(73, \cdot)\) n/a 3776 16
4725.2.gd \(\chi_{4725}(131, \cdot)\) n/a 17184 24
4725.2.gg \(\chi_{4725}(4, \cdot)\) n/a 17184 24
4725.2.gi \(\chi_{4725}(169, \cdot)\) n/a 12960 24
4725.2.gk \(\chi_{4725}(236, \cdot)\) n/a 17184 24
4725.2.gm \(\chi_{4725}(41, \cdot)\) n/a 17184 24
4725.2.gn \(\chi_{4725}(184, \cdot)\) n/a 17184 24
4725.2.gr \(\chi_{4725}(59, \cdot)\) n/a 17184 24
4725.2.gt \(\chi_{4725}(104, \cdot)\) n/a 17184 24
4725.2.gw \(\chi_{4725}(164, \cdot)\) n/a 17184 24
4725.2.gz \(\chi_{4725}(52, \cdot)\) n/a 34368 48
4725.2.ha \(\chi_{4725}(92, \cdot)\) n/a 25920 48
4725.2.hc \(\chi_{4725}(2, \cdot)\) n/a 34368 48
4725.2.he \(\chi_{4725}(13, \cdot)\) n/a 34368 48
4725.2.hg \(\chi_{4725}(187, \cdot)\) n/a 34368 48
4725.2.hj \(\chi_{4725}(23, \cdot)\) n/a 34368 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4725))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4725)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(945))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)\(^{\oplus 2}\)