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Properties

Label 4675.2
Level 4675
Weight 2
Dimension 772072
Nonzero newspaces 126
Sturm bound 3456000

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Defining parameters

Level: \( N \) = \( 4675 = 5^{2} \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 126 \)
Sturm bound: \(3456000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4675))\).

Total New Old
Modular forms 872960 783144 89816
Cusp forms 855041 772072 82969
Eisenstein series 17919 11072 6847

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4675))\)

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
4675.2.a \(\chi_{4675}(1, \cdot)\) 4675.2.a.a 1 1
4675.2.a.b 1
4675.2.a.c 1
4675.2.a.d 1
4675.2.a.e 1
4675.2.a.f 1
4675.2.a.g 1
4675.2.a.h 1
4675.2.a.i 1
4675.2.a.j 1
4675.2.a.k 1
4675.2.a.l 1
4675.2.a.m 1
4675.2.a.n 1
4675.2.a.o 1
4675.2.a.p 1
4675.2.a.q 1
4675.2.a.r 1
4675.2.a.s 1
4675.2.a.t 1
4675.2.a.u 2
4675.2.a.v 2
4675.2.a.w 3
4675.2.a.x 3
4675.2.a.y 3
4675.2.a.z 3
4675.2.a.ba 3
4675.2.a.bb 3
4675.2.a.bc 3
4675.2.a.bd 4
4675.2.a.be 4
4675.2.a.bf 5
4675.2.a.bg 5
4675.2.a.bh 6
4675.2.a.bi 9
4675.2.a.bj 11
4675.2.a.bk 11
4675.2.a.bl 11
4675.2.a.bm 11
4675.2.a.bn 12
4675.2.a.bo 12
4675.2.a.bp 13
4675.2.a.bq 13
4675.2.a.br 18
4675.2.a.bs 18
4675.2.a.bt 22
4675.2.a.bu 22
4675.2.b \(\chi_{4675}(749, \cdot)\) n/a 240 1
4675.2.e \(\chi_{4675}(2124, \cdot)\) n/a 272 1
4675.2.f \(\chi_{4675}(1376, \cdot)\) n/a 284 1
4675.2.i \(\chi_{4675}(276, \cdot)\) n/a 568 2
4675.2.l \(\chi_{4675}(582, \cdot)\) n/a 640 2
4675.2.m \(\chi_{4675}(307, \cdot)\) n/a 576 2
4675.2.p \(\chi_{4675}(1682, \cdot)\) n/a 640 2
4675.2.q \(\chi_{4675}(1143, \cdot)\) n/a 640 2
4675.2.s \(\chi_{4675}(1024, \cdot)\) n/a 544 2
4675.2.u \(\chi_{4675}(86, \cdot)\) n/a 1920 4
4675.2.v \(\chi_{4675}(851, \cdot)\) n/a 1216 4
4675.2.w \(\chi_{4675}(936, \cdot)\) n/a 1600 4
4675.2.x \(\chi_{4675}(511, \cdot)\) n/a 1920 4
4675.2.y \(\chi_{4675}(1021, \cdot)\) n/a 1920 4
4675.2.z \(\chi_{4675}(1191, \cdot)\) n/a 1920 4
4675.2.bb \(\chi_{4675}(593, \cdot)\) n/a 1280 4
4675.2.bc \(\chi_{4675}(1651, \cdot)\) n/a 1144 4
4675.2.be \(\chi_{4675}(474, \cdot)\) n/a 1072 4
4675.2.bh \(\chi_{4675}(32, \cdot)\) n/a 1280 4
4675.2.bi \(\chi_{4675}(509, \cdot)\) n/a 2144 4
4675.2.bl \(\chi_{4675}(664, \cdot)\) n/a 1920 4
4675.2.bn \(\chi_{4675}(1291, \cdot)\) n/a 2144 4
4675.2.bt \(\chi_{4675}(356, \cdot)\) n/a 2144 4
4675.2.bu \(\chi_{4675}(441, \cdot)\) n/a 1808 4
4675.2.bx \(\chi_{4675}(526, \cdot)\) n/a 1344 4
4675.2.by \(\chi_{4675}(16, \cdot)\) n/a 2144 4
4675.2.cc \(\chi_{4675}(1939, \cdot)\) n/a 1920 4
4675.2.cd \(\chi_{4675}(169, \cdot)\) n/a 2144 4
4675.2.cg \(\chi_{4675}(339, \cdot)\) n/a 2144 4
4675.2.ch \(\chi_{4675}(1274, \cdot)\) n/a 1280 4
4675.2.ck \(\chi_{4675}(254, \cdot)\) n/a 1792 4
4675.2.cl \(\chi_{4675}(1684, \cdot)\) n/a 1600 4
4675.2.co \(\chi_{4675}(324, \cdot)\) n/a 1152 4
4675.2.cp \(\chi_{4675}(69, \cdot)\) n/a 1920 4
4675.2.cs \(\chi_{4675}(834, \cdot)\) n/a 1920 4
4675.2.ct \(\chi_{4675}(3314, \cdot)\) n/a 2144 4
4675.2.cx \(\chi_{4675}(2566, \cdot)\) n/a 2144 4
4675.2.cz \(\chi_{4675}(232, \cdot)\) n/a 2160 8
4675.2.da \(\chi_{4675}(351, \cdot)\) n/a 2688 8
4675.2.dd \(\chi_{4675}(549, \cdot)\) n/a 2560 8
4675.2.de \(\chi_{4675}(507, \cdot)\) n/a 2160 8
4675.2.dg \(\chi_{4675}(1466, \cdot)\) n/a 4288 8
4675.2.dj \(\chi_{4675}(2214, \cdot)\) n/a 4288 8
4675.2.dl \(\chi_{4675}(89, \cdot)\) n/a 3584 8
4675.2.dp \(\chi_{4675}(489, \cdot)\) n/a 4288 8
4675.2.dq \(\chi_{4675}(4, \cdot)\) n/a 4288 8
4675.2.dr \(\chi_{4675}(174, \cdot)\) n/a 2560 8
4675.2.ds \(\chi_{4675}(327, \cdot)\) n/a 4288 8
4675.2.dv \(\chi_{4675}(888, \cdot)\) n/a 4288 8
4675.2.dw \(\chi_{4675}(208, \cdot)\) n/a 4288 8
4675.2.ea \(\chi_{4675}(293, \cdot)\) n/a 2560 8
4675.2.eb \(\chi_{4675}(387, \cdot)\) n/a 4288 8
4675.2.ec \(\chi_{4675}(123, \cdot)\) n/a 4288 8
4675.2.ee \(\chi_{4675}(1172, \cdot)\) n/a 4288 8
4675.2.eh \(\chi_{4675}(613, \cdot)\) n/a 3840 8
4675.2.ei \(\chi_{4675}(392, \cdot)\) n/a 3840 8
4675.2.ek \(\chi_{4675}(1427, \cdot)\) n/a 4288 8
4675.2.em \(\chi_{4675}(118, \cdot)\) n/a 2560 8
4675.2.en \(\chi_{4675}(373, \cdot)\) n/a 4288 8
4675.2.eo \(\chi_{4675}(237, \cdot)\) n/a 4288 8
4675.2.et \(\chi_{4675}(52, \cdot)\) n/a 3840 8
4675.2.ex \(\chi_{4675}(18, \cdot)\) n/a 2304 8
4675.2.ey \(\chi_{4675}(953, \cdot)\) n/a 3840 8
4675.2.ez \(\chi_{4675}(1242, \cdot)\) n/a 3840 8
4675.2.fb \(\chi_{4675}(288, \cdot)\) n/a 4288 8
4675.2.fc \(\chi_{4675}(72, \cdot)\) n/a 4288 8
4675.2.ff \(\chi_{4675}(948, \cdot)\) n/a 4288 8
4675.2.fg \(\chi_{4675}(13, \cdot)\) n/a 4288 8
4675.2.fh \(\chi_{4675}(1007, \cdot)\) n/a 2560 8
4675.2.fl \(\chi_{4675}(98, \cdot)\) n/a 4288 8
4675.2.fn \(\chi_{4675}(633, \cdot)\) n/a 4288 8
4675.2.fp \(\chi_{4675}(191, \cdot)\) n/a 4288 8
4675.2.ft \(\chi_{4675}(81, \cdot)\) n/a 4288 8
4675.2.fu \(\chi_{4675}(361, \cdot)\) n/a 4288 8
4675.2.fv \(\chi_{4675}(251, \cdot)\) n/a 2688 8
4675.2.fx \(\chi_{4675}(166, \cdot)\) n/a 3616 8
4675.2.fy \(\chi_{4675}(234, \cdot)\) n/a 4288 8
4675.2.ga \(\chi_{4675}(162, \cdot)\) n/a 8576 16
4675.2.gd \(\chi_{4675}(178, \cdot)\) n/a 8576 16
4675.2.ge \(\chi_{4675}(87, \cdot)\) n/a 8576 16
4675.2.gf \(\chi_{4675}(117, \cdot)\) n/a 8576 16
4675.2.gg \(\chi_{4675}(2, \cdot)\) n/a 8576 16
4675.2.gl \(\chi_{4675}(457, \cdot)\) n/a 5120 16
4675.2.gn \(\chi_{4675}(104, \cdot)\) n/a 8576 16
4675.2.gp \(\chi_{4675}(366, \cdot)\) n/a 8576 16
4675.2.gr \(\chi_{4675}(36, \cdot)\) n/a 8576 16
4675.2.gt \(\chi_{4675}(144, \cdot)\) n/a 7232 16
4675.2.gu \(\chi_{4675}(49, \cdot)\) n/a 5120 16
4675.2.gx \(\chi_{4675}(9, \cdot)\) n/a 8576 16
4675.2.gy \(\chi_{4675}(434, \cdot)\) n/a 8576 16
4675.2.ha \(\chi_{4675}(26, \cdot)\) n/a 5376 16
4675.2.hd \(\chi_{4675}(246, \cdot)\) n/a 8576 16
4675.2.he \(\chi_{4675}(236, \cdot)\) n/a 8576 16
4675.2.hh \(\chi_{4675}(111, \cdot)\) n/a 7168 16
4675.2.hj \(\chi_{4675}(59, \cdot)\) n/a 8576 16
4675.2.hl \(\chi_{4675}(138, \cdot)\) n/a 8576 16
4675.2.hm \(\chi_{4675}(127, \cdot)\) n/a 8576 16
4675.2.hn \(\chi_{4675}(83, \cdot)\) n/a 8576 16
4675.2.ho \(\chi_{4675}(417, \cdot)\) n/a 8576 16
4675.2.ht \(\chi_{4675}(332, \cdot)\) n/a 5120 16
4675.2.hu \(\chi_{4675}(348, \cdot)\) n/a 8576 16
4675.2.hw \(\chi_{4675}(258, \cdot)\) n/a 17152 32
4675.2.hy \(\chi_{4675}(108, \cdot)\) n/a 17152 32
4675.2.ie \(\chi_{4675}(12, \cdot)\) n/a 14400 32
4675.2.if \(\chi_{4675}(82, \cdot)\) n/a 10240 32
4675.2.ig \(\chi_{4675}(163, \cdot)\) n/a 17152 32
4675.2.ih \(\chi_{4675}(58, \cdot)\) n/a 17152 32
4675.2.ii \(\chi_{4675}(139, \cdot)\) n/a 17152 32
4675.2.il \(\chi_{4675}(41, \cdot)\) n/a 17152 32
4675.2.in \(\chi_{4675}(131, \cdot)\) n/a 17152 32
4675.2.ip \(\chi_{4675}(79, \cdot)\) n/a 17152 32
4675.2.iq \(\chi_{4675}(29, \cdot)\) n/a 17152 32
4675.2.it \(\chi_{4675}(24, \cdot)\) n/a 10240 32
4675.2.iu \(\chi_{4675}(39, \cdot)\) n/a 17152 32
4675.2.ix \(\chi_{4675}(61, \cdot)\) n/a 17152 32
4675.2.iy \(\chi_{4675}(226, \cdot)\) n/a 10752 32
4675.2.jb \(\chi_{4675}(6, \cdot)\) n/a 17152 32
4675.2.jc \(\chi_{4675}(116, \cdot)\) n/a 17152 32
4675.2.je \(\chi_{4675}(54, \cdot)\) n/a 17152 32
4675.2.jh \(\chi_{4675}(48, \cdot)\) n/a 17152 32
4675.2.ji \(\chi_{4675}(147, \cdot)\) n/a 17152 32
4675.2.jj \(\chi_{4675}(218, \cdot)\) n/a 10240 32
4675.2.jk \(\chi_{4675}(133, \cdot)\) n/a 14400 32
4675.2.jl \(\chi_{4675}(3, \cdot)\) n/a 17152 32
4675.2.jr \(\chi_{4675}(37, \cdot)\) n/a 17152 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4675))\)\(^{\oplus 1}\)