Properties

Label 6300.2
Level 6300
Weight 2
Dimension 421060
Nonzero newspaces 120
Sturm bound 4147200

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Defining parameters

Level: \( N \) = \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(4147200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6300))\).

Total New Old
Modular forms 1050240 424752 625488
Cusp forms 1023361 421060 602301
Eisenstein series 26879 3692 23187

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6300))\)

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
6300.2.a \(\chi_{6300}(1, \cdot)\) 6300.2.a.a 1 1
6300.2.a.b 1
6300.2.a.c 1
6300.2.a.d 1
6300.2.a.e 1
6300.2.a.f 1
6300.2.a.g 1
6300.2.a.h 1
6300.2.a.i 1
6300.2.a.j 1
6300.2.a.k 1
6300.2.a.l 1
6300.2.a.m 1
6300.2.a.n 1
6300.2.a.o 1
6300.2.a.p 1
6300.2.a.q 1
6300.2.a.r 1
6300.2.a.s 1
6300.2.a.t 1
6300.2.a.u 1
6300.2.a.v 1
6300.2.a.w 1
6300.2.a.x 1
6300.2.a.y 1
6300.2.a.z 1
6300.2.a.ba 1
6300.2.a.bb 1
6300.2.a.bc 1
6300.2.a.bd 1
6300.2.a.be 1
6300.2.a.bf 1
6300.2.a.bg 2
6300.2.a.bh 2
6300.2.a.bi 2
6300.2.a.bj 2
6300.2.a.bk 4
6300.2.a.bl 4
6300.2.c \(\chi_{6300}(5851, \cdot)\) n/a 374 1
6300.2.d \(\chi_{6300}(3401, \cdot)\) 6300.2.d.a 4 1
6300.2.d.b 4
6300.2.d.c 4
6300.2.d.d 12
6300.2.d.e 12
6300.2.d.f 16
6300.2.f \(\chi_{6300}(3149, \cdot)\) 6300.2.f.a 8 1
6300.2.f.b 8
6300.2.f.c 8
6300.2.f.d 24
6300.2.i \(\chi_{6300}(5599, \cdot)\) n/a 356 1
6300.2.k \(\chi_{6300}(6049, \cdot)\) 6300.2.k.a 2 1
6300.2.k.b 2
6300.2.k.c 2
6300.2.k.d 2
6300.2.k.e 2
6300.2.k.f 2
6300.2.k.g 2
6300.2.k.h 2
6300.2.k.i 2
6300.2.k.j 2
6300.2.k.k 2
6300.2.k.l 2
6300.2.k.m 2
6300.2.k.n 2
6300.2.k.o 2
6300.2.k.p 2
6300.2.k.q 2
6300.2.k.r 2
6300.2.k.s 4
6300.2.k.t 4
6300.2.l \(\chi_{6300}(3599, \cdot)\) n/a 216 1
6300.2.n \(\chi_{6300}(3851, \cdot)\) n/a 228 1
6300.2.q \(\chi_{6300}(3301, \cdot)\) n/a 304 2
6300.2.r \(\chi_{6300}(2101, \cdot)\) n/a 228 2
6300.2.s \(\chi_{6300}(1801, \cdot)\) n/a 126 2
6300.2.t \(\chi_{6300}(1201, \cdot)\) n/a 304 2
6300.2.v \(\chi_{6300}(1457, \cdot)\) 6300.2.v.a 4 2
6300.2.v.b 4
6300.2.v.c 4
6300.2.v.d 4
6300.2.v.e 12
6300.2.v.f 12
6300.2.v.g 16
6300.2.v.h 16
6300.2.w \(\chi_{6300}(2143, \cdot)\) n/a 540 2
6300.2.z \(\chi_{6300}(1007, \cdot)\) n/a 576 2
6300.2.ba \(\chi_{6300}(1693, \cdot)\) n/a 120 2
6300.2.bc \(\chi_{6300}(1261, \cdot)\) n/a 296 4
6300.2.bd \(\chi_{6300}(1699, \cdot)\) n/a 1712 2
6300.2.bg \(\chi_{6300}(1949, \cdot)\) n/a 288 2
6300.2.bi \(\chi_{6300}(2201, \cdot)\) n/a 304 2
6300.2.bj \(\chi_{6300}(1951, \cdot)\) n/a 1800 2
6300.2.bm \(\chi_{6300}(2699, \cdot)\) n/a 576 2
6300.2.bn \(\chi_{6300}(1549, \cdot)\) n/a 120 2
6300.2.bp \(\chi_{6300}(1751, \cdot)\) n/a 1368 2
6300.2.bt \(\chi_{6300}(3551, \cdot)\) n/a 1800 2
6300.2.bw \(\chi_{6300}(1849, \cdot)\) n/a 216 2
6300.2.by \(\chi_{6300}(3299, \cdot)\) n/a 1712 2
6300.2.bz \(\chi_{6300}(3049, \cdot)\) n/a 288 2
6300.2.cb \(\chi_{6300}(1499, \cdot)\) n/a 1296 2
6300.2.cf \(\chi_{6300}(2951, \cdot)\) n/a 608 2
6300.2.ch \(\chi_{6300}(1601, \cdot)\) 6300.2.ch.a 4 2
6300.2.ch.b 12
6300.2.ch.c 12
6300.2.ch.d 20
6300.2.ch.e 20
6300.2.ch.f 32
6300.2.ci \(\chi_{6300}(451, \cdot)\) n/a 748 2
6300.2.ck \(\chi_{6300}(1049, \cdot)\) n/a 288 2
6300.2.cm \(\chi_{6300}(4399, \cdot)\) n/a 1712 2
6300.2.cp \(\chi_{6300}(5549, \cdot)\) n/a 288 2
6300.2.cr \(\chi_{6300}(1399, \cdot)\) n/a 1712 2
6300.2.ct \(\chi_{6300}(1651, \cdot)\) n/a 1800 2
6300.2.cv \(\chi_{6300}(101, \cdot)\) n/a 304 2
6300.2.cw \(\chi_{6300}(4651, \cdot)\) n/a 1800 2
6300.2.cy \(\chi_{6300}(1301, \cdot)\) n/a 304 2
6300.2.da \(\chi_{6300}(199, \cdot)\) n/a 712 2
6300.2.dd \(\chi_{6300}(1349, \cdot)\) 6300.2.dd.a 8 2
6300.2.dd.b 24
6300.2.dd.c 24
6300.2.dd.d 40
6300.2.dg \(\chi_{6300}(851, \cdot)\) n/a 1800 2
6300.2.di \(\chi_{6300}(599, \cdot)\) n/a 1712 2
6300.2.dj \(\chi_{6300}(949, \cdot)\) n/a 288 2
6300.2.dn \(\chi_{6300}(71, \cdot)\) n/a 1440 4
6300.2.dp \(\chi_{6300}(1079, \cdot)\) n/a 1440 4
6300.2.dq \(\chi_{6300}(1009, \cdot)\) n/a 304 4
6300.2.ds \(\chi_{6300}(559, \cdot)\) n/a 2384 4
6300.2.dv \(\chi_{6300}(629, \cdot)\) n/a 320 4
6300.2.dx \(\chi_{6300}(881, \cdot)\) n/a 320 4
6300.2.dy \(\chi_{6300}(811, \cdot)\) n/a 2384 4
6300.2.eb \(\chi_{6300}(1843, \cdot)\) n/a 3424 4
6300.2.ec \(\chi_{6300}(2993, \cdot)\) n/a 576 4
6300.2.ee \(\chi_{6300}(1343, \cdot)\) n/a 3424 4
6300.2.eg \(\chi_{6300}(1657, \cdot)\) n/a 240 4
6300.2.ei \(\chi_{6300}(493, \cdot)\) n/a 576 4
6300.2.el \(\chi_{6300}(1643, \cdot)\) n/a 3424 4
6300.2.en \(\chi_{6300}(143, \cdot)\) n/a 1152 4
6300.2.ep \(\chi_{6300}(1357, \cdot)\) n/a 576 4
6300.2.eq \(\chi_{6300}(1793, \cdot)\) n/a 432 4
6300.2.es \(\chi_{6300}(1243, \cdot)\) n/a 1424 4
6300.2.eu \(\chi_{6300}(907, \cdot)\) n/a 3424 4
6300.2.ex \(\chi_{6300}(893, \cdot)\) n/a 576 4
6300.2.ez \(\chi_{6300}(557, \cdot)\) n/a 192 4
6300.2.fb \(\chi_{6300}(43, \cdot)\) n/a 2592 4
6300.2.fd \(\chi_{6300}(157, \cdot)\) n/a 576 4
6300.2.fe \(\chi_{6300}(1307, \cdot)\) n/a 3424 4
6300.2.fg \(\chi_{6300}(961, \cdot)\) n/a 1920 8
6300.2.fh \(\chi_{6300}(361, \cdot)\) n/a 800 8
6300.2.fi \(\chi_{6300}(421, \cdot)\) n/a 1440 8
6300.2.fj \(\chi_{6300}(121, \cdot)\) n/a 1920 8
6300.2.fl \(\chi_{6300}(433, \cdot)\) n/a 800 8
6300.2.fm \(\chi_{6300}(503, \cdot)\) n/a 3840 8
6300.2.fp \(\chi_{6300}(127, \cdot)\) n/a 3600 8
6300.2.fq \(\chi_{6300}(197, \cdot)\) n/a 480 8
6300.2.ft \(\chi_{6300}(709, \cdot)\) n/a 1920 8
6300.2.fu \(\chi_{6300}(1859, \cdot)\) n/a 11456 8
6300.2.fw \(\chi_{6300}(191, \cdot)\) n/a 11456 8
6300.2.fz \(\chi_{6300}(89, \cdot)\) n/a 640 8
6300.2.gc \(\chi_{6300}(19, \cdot)\) n/a 4768 8
6300.2.ge \(\chi_{6300}(41, \cdot)\) n/a 1920 8
6300.2.gg \(\chi_{6300}(871, \cdot)\) n/a 11456 8
6300.2.gh \(\chi_{6300}(761, \cdot)\) n/a 1920 8
6300.2.gj \(\chi_{6300}(391, \cdot)\) n/a 11456 8
6300.2.gl \(\chi_{6300}(139, \cdot)\) n/a 11456 8
6300.2.gn \(\chi_{6300}(509, \cdot)\) n/a 1920 8
6300.2.gq \(\chi_{6300}(619, \cdot)\) n/a 11456 8
6300.2.gs \(\chi_{6300}(209, \cdot)\) n/a 1920 8
6300.2.gu \(\chi_{6300}(271, \cdot)\) n/a 4768 8
6300.2.gv \(\chi_{6300}(341, \cdot)\) n/a 640 8
6300.2.gx \(\chi_{6300}(431, \cdot)\) n/a 3840 8
6300.2.hb \(\chi_{6300}(239, \cdot)\) n/a 8640 8
6300.2.hd \(\chi_{6300}(529, \cdot)\) n/a 1920 8
6300.2.he \(\chi_{6300}(779, \cdot)\) n/a 11456 8
6300.2.hg \(\chi_{6300}(169, \cdot)\) n/a 1440 8
6300.2.hj \(\chi_{6300}(11, \cdot)\) n/a 11456 8
6300.2.hn \(\chi_{6300}(491, \cdot)\) n/a 8640 8
6300.2.hp \(\chi_{6300}(109, \cdot)\) n/a 800 8
6300.2.hq \(\chi_{6300}(179, \cdot)\) n/a 3840 8
6300.2.ht \(\chi_{6300}(31, \cdot)\) n/a 11456 8
6300.2.hu \(\chi_{6300}(941, \cdot)\) n/a 1920 8
6300.2.hw \(\chi_{6300}(689, \cdot)\) n/a 1920 8
6300.2.hz \(\chi_{6300}(439, \cdot)\) n/a 11456 8
6300.2.ib \(\chi_{6300}(47, \cdot)\) n/a 22912 16
6300.2.ic \(\chi_{6300}(313, \cdot)\) n/a 3840 16
6300.2.ie \(\chi_{6300}(463, \cdot)\) n/a 17280 16
6300.2.ig \(\chi_{6300}(53, \cdot)\) n/a 1280 16
6300.2.ii \(\chi_{6300}(137, \cdot)\) n/a 3840 16
6300.2.il \(\chi_{6300}(247, \cdot)\) n/a 22912 16
6300.2.in \(\chi_{6300}(163, \cdot)\) n/a 9536 16
6300.2.ip \(\chi_{6300}(113, \cdot)\) n/a 2880 16
6300.2.iq \(\chi_{6300}(13, \cdot)\) n/a 3840 16
6300.2.is \(\chi_{6300}(467, \cdot)\) n/a 7680 16
6300.2.iu \(\chi_{6300}(227, \cdot)\) n/a 22912 16
6300.2.ix \(\chi_{6300}(733, \cdot)\) n/a 3840 16
6300.2.iz \(\chi_{6300}(73, \cdot)\) n/a 1600 16
6300.2.jb \(\chi_{6300}(83, \cdot)\) n/a 22912 16
6300.2.jd \(\chi_{6300}(317, \cdot)\) n/a 3840 16
6300.2.je \(\chi_{6300}(67, \cdot)\) n/a 22912 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3150))\)\(^{\oplus 2}\)