# Properties

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

## 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

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