# Properties

 Label 6384.2 Level 6384 Weight 2 Dimension 443108 Nonzero newspaces 128 Sturm bound 4423680

## Defining parameters

 Level: $$N$$ = $$6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$128$$ Sturm bound: $$4423680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6384))$$.

Total New Old
Modular forms 1118016 446164 671852
Cusp forms 1093825 443108 650717
Eisenstein series 24191 3056 21135

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6384))$$

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
6384.2.a $$\chi_{6384}(1, \cdot)$$ 6384.2.a.a 1 1
6384.2.a.b 1
6384.2.a.c 1
6384.2.a.d 1
6384.2.a.e 1
6384.2.a.f 1
6384.2.a.g 1
6384.2.a.h 1
6384.2.a.i 1
6384.2.a.j 1
6384.2.a.k 1
6384.2.a.l 1
6384.2.a.m 1
6384.2.a.n 1
6384.2.a.o 1
6384.2.a.p 1
6384.2.a.q 1
6384.2.a.r 1
6384.2.a.s 1
6384.2.a.t 1
6384.2.a.u 1
6384.2.a.v 1
6384.2.a.w 1
6384.2.a.x 1
6384.2.a.y 1
6384.2.a.z 1
6384.2.a.ba 1
6384.2.a.bb 1
6384.2.a.bc 1
6384.2.a.bd 1
6384.2.a.be 1
6384.2.a.bf 1
6384.2.a.bg 1
6384.2.a.bh 2
6384.2.a.bi 2
6384.2.a.bj 2
6384.2.a.bk 2
6384.2.a.bl 2
6384.2.a.bm 2
6384.2.a.bn 2
6384.2.a.bo 2
6384.2.a.bp 2
6384.2.a.bq 2
6384.2.a.br 2
6384.2.a.bs 2
6384.2.a.bt 3
6384.2.a.bu 3
6384.2.a.bv 3
6384.2.a.bw 3
6384.2.a.bx 3
6384.2.a.by 4
6384.2.a.bz 4
6384.2.a.ca 4
6384.2.a.cb 4
6384.2.a.cc 5
6384.2.a.cd 5
6384.2.a.ce 5
6384.2.a.cf 5
6384.2.b $$\chi_{6384}(113, \cdot)$$ n/a 240 1
6384.2.c $$\chi_{6384}(6271, \cdot)$$ n/a 144 1
6384.2.d $$\chi_{6384}(3191, \cdot)$$ None 0 1
6384.2.e $$\chi_{6384}(3193, \cdot)$$ None 0 1
6384.2.n $$\chi_{6384}(2927, \cdot)$$ n/a 216 1
6384.2.o $$\chi_{6384}(3457, \cdot)$$ n/a 160 1
6384.2.p $$\chi_{6384}(4409, \cdot)$$ None 0 1
6384.2.q $$\chi_{6384}(1975, \cdot)$$ None 0 1
6384.2.r $$\chi_{6384}(6119, \cdot)$$ None 0 1
6384.2.s $$\chi_{6384}(265, \cdot)$$ None 0 1
6384.2.t $$\chi_{6384}(1217, \cdot)$$ n/a 288 1
6384.2.u $$\chi_{6384}(5167, \cdot)$$ n/a 120 1
6384.2.bd $$\chi_{6384}(3305, \cdot)$$ None 0 1
6384.2.be $$\chi_{6384}(3079, \cdot)$$ None 0 1
6384.2.bf $$\chi_{6384}(6383, \cdot)$$ n/a 320 1
6384.2.bg $$\chi_{6384}(961, \cdot)$$ n/a 320 2
6384.2.bh $$\chi_{6384}(3649, \cdot)$$ n/a 288 2
6384.2.bi $$\chi_{6384}(3697, \cdot)$$ n/a 240 2
6384.2.bj $$\chi_{6384}(1873, \cdot)$$ n/a 320 2
6384.2.bl $$\chi_{6384}(1331, \cdot)$$ n/a 1728 2
6384.2.bm $$\chi_{6384}(1861, \cdot)$$ n/a 1280 2
6384.2.bo $$\chi_{6384}(1709, \cdot)$$ n/a 1920 2
6384.2.br $$\chi_{6384}(1483, \cdot)$$ n/a 1152 2
6384.2.bs $$\chi_{6384}(1595, \cdot)$$ n/a 2544 2
6384.2.bv $$\chi_{6384}(1597, \cdot)$$ n/a 864 2
6384.2.bx $$\chi_{6384}(2813, \cdot)$$ n/a 2304 2
6384.2.by $$\chi_{6384}(379, \cdot)$$ n/a 960 2
6384.2.ca $$\chi_{6384}(2839, \cdot)$$ None 0 2
6384.2.cb $$\chi_{6384}(425, \cdot)$$ None 0 2
6384.2.cc $$\chi_{6384}(145, \cdot)$$ n/a 320 2
6384.2.cd $$\chi_{6384}(4799, \cdot)$$ n/a 640 2
6384.2.cm $$\chi_{6384}(121, \cdot)$$ None 0 2
6384.2.cn $$\chi_{6384}(1319, \cdot)$$ None 0 2
6384.2.co $$\chi_{6384}(2287, \cdot)$$ n/a 320 2
6384.2.cp $$\chi_{6384}(977, \cdot)$$ n/a 632 2
6384.2.cu $$\chi_{6384}(881, \cdot)$$ n/a 632 2
6384.2.cv $$\chi_{6384}(1471, \cdot)$$ n/a 240 2
6384.2.cw $$\chi_{6384}(3431, \cdot)$$ None 0 2
6384.2.cx $$\chi_{6384}(601, \cdot)$$ None 0 2
6384.2.dc $$\chi_{6384}(3127, \cdot)$$ None 0 2
6384.2.dd $$\chi_{6384}(1817, \cdot)$$ None 0 2
6384.2.de $$\chi_{6384}(2159, \cdot)$$ n/a 640 2
6384.2.dj $$\chi_{6384}(1823, \cdot)$$ n/a 640 2
6384.2.dk $$\chi_{6384}(4903, \cdot)$$ None 0 2
6384.2.dl $$\chi_{6384}(569, \cdot)$$ None 0 2
6384.2.dm $$\chi_{6384}(2431, \cdot)$$ n/a 320 2
6384.2.dn $$\chi_{6384}(3041, \cdot)$$ n/a 576 2
6384.2.do $$\chi_{6384}(2089, \cdot)$$ None 0 2
6384.2.dp $$\chi_{6384}(3383, \cdot)$$ None 0 2
6384.2.du $$\chi_{6384}(2425, \cdot)$$ None 0 2
6384.2.dv $$\chi_{6384}(695, \cdot)$$ None 0 2
6384.2.dw $$\chi_{6384}(3679, \cdot)$$ n/a 320 2
6384.2.dx $$\chi_{6384}(1265, \cdot)$$ n/a 632 2
6384.2.ec $$\chi_{6384}(335, \cdot)$$ n/a 640 2
6384.2.ed $$\chi_{6384}(3641, \cdot)$$ None 0 2
6384.2.ee $$\chi_{6384}(391, \cdot)$$ None 0 2
6384.2.en $$\chi_{6384}(3527, \cdot)$$ None 0 2
6384.2.eo $$\chi_{6384}(505, \cdot)$$ None 0 2
6384.2.ep $$\chi_{6384}(449, \cdot)$$ n/a 480 2
6384.2.eq $$\chi_{6384}(3583, \cdot)$$ n/a 320 2
6384.2.ev $$\chi_{6384}(2497, \cdot)$$ n/a 320 2
6384.2.ew $$\chi_{6384}(767, \cdot)$$ n/a 640 2
6384.2.ex $$\chi_{6384}(487, \cdot)$$ None 0 2
6384.2.ey $$\chi_{6384}(4457, \cdot)$$ None 0 2
6384.2.fd $$\chi_{6384}(151, \cdot)$$ None 0 2
6384.2.fe $$\chi_{6384}(761, \cdot)$$ None 0 2
6384.2.ff $$\chi_{6384}(5281, \cdot)$$ n/a 320 2
6384.2.fg $$\chi_{6384}(191, \cdot)$$ n/a 576 2
6384.2.fh $$\chi_{6384}(457, \cdot)$$ None 0 2
6384.2.fi $$\chi_{6384}(5015, \cdot)$$ None 0 2
6384.2.fj $$\chi_{6384}(1711, \cdot)$$ n/a 288 2
6384.2.fk $$\chi_{6384}(3761, \cdot)$$ n/a 632 2
6384.2.fp $$\chi_{6384}(1375, \cdot)$$ n/a 320 2
6384.2.fq $$\chi_{6384}(65, \cdot)$$ n/a 632 2
6384.2.fr $$\chi_{6384}(1033, \cdot)$$ None 0 2
6384.2.fs $$\chi_{6384}(2231, \cdot)$$ None 0 2
6384.2.fx $$\chi_{6384}(1721, \cdot)$$ None 0 2
6384.2.fy $$\chi_{6384}(2311, \cdot)$$ None 0 2
6384.2.fz $$\chi_{6384}(239, \cdot)$$ n/a 480 2
6384.2.ga $$\chi_{6384}(3793, \cdot)$$ n/a 320 2
6384.2.gf $$\chi_{6384}(3071, \cdot)$$ n/a 640 2
6384.2.gg $$\chi_{6384}(2215, \cdot)$$ None 0 2
6384.2.gh $$\chi_{6384}(905, \cdot)$$ None 0 2
6384.2.gq $$\chi_{6384}(2767, \cdot)$$ n/a 320 2
6384.2.gr $$\chi_{6384}(353, \cdot)$$ n/a 632 2
6384.2.gs $$\chi_{6384}(3337, \cdot)$$ None 0 2
6384.2.gt $$\chi_{6384}(1607, \cdot)$$ None 0 2
6384.2.gu $$\chi_{6384}(1681, \cdot)$$ n/a 720 6
6384.2.gv $$\chi_{6384}(289, \cdot)$$ n/a 960 6
6384.2.gw $$\chi_{6384}(625, \cdot)$$ n/a 960 6
6384.2.gx $$\chi_{6384}(829, \cdot)$$ n/a 2560 4
6384.2.ha $$\chi_{6384}(2291, \cdot)$$ n/a 5088 4
6384.2.hc $$\chi_{6384}(1531, \cdot)$$ n/a 2560 4
6384.2.hd $$\chi_{6384}(221, \cdot)$$ n/a 5088 4
6384.2.hg $$\chi_{6384}(1171, \cdot)$$ n/a 2560 4
6384.2.hh $$\chi_{6384}(1949, \cdot)$$ n/a 5088 4
6384.2.hj $$\chi_{6384}(125, \cdot)$$ n/a 5088 4
6384.2.hm $$\chi_{6384}(835, \cdot)$$ n/a 2560 4
6384.2.hn $$\chi_{6384}(1445, \cdot)$$ n/a 4608 4
6384.2.hq $$\chi_{6384}(715, \cdot)$$ n/a 1920 4
6384.2.hr $$\chi_{6384}(277, \cdot)$$ n/a 2560 4
6384.2.hu $$\chi_{6384}(1475, \cdot)$$ n/a 5088 4
6384.2.hw $$\chi_{6384}(1091, \cdot)$$ n/a 5088 4
6384.2.hx $$\chi_{6384}(2053, \cdot)$$ n/a 2304 4
6384.2.ia $$\chi_{6384}(227, \cdot)$$ n/a 5088 4
6384.2.ib $$\chi_{6384}(1261, \cdot)$$ n/a 1920 4
6384.2.id $$\chi_{6384}(619, \cdot)$$ n/a 2560 4
6384.2.ig $$\chi_{6384}(2501, \cdot)$$ n/a 5088 4
6384.2.ii $$\chi_{6384}(1205, \cdot)$$ n/a 3840 4
6384.2.ij $$\chi_{6384}(115, \cdot)$$ n/a 2304 4
6384.2.im $$\chi_{6384}(2165, \cdot)$$ n/a 5088 4
6384.2.in $$\chi_{6384}(1147, \cdot)$$ n/a 2560 4
6384.2.iq $$\chi_{6384}(1741, \cdot)$$ n/a 2560 4
6384.2.ir $$\chi_{6384}(11, \cdot)$$ n/a 5088 4
6384.2.it $$\chi_{6384}(995, \cdot)$$ n/a 3840 4
6384.2.iw $$\chi_{6384}(493, \cdot)$$ n/a 2560 4
6384.2.ix $$\chi_{6384}(1787, \cdot)$$ n/a 4608 4
6384.2.ja $$\chi_{6384}(1357, \cdot)$$ n/a 2560 4
6384.2.jc $$\chi_{6384}(2557, \cdot)$$ n/a 2560 4
6384.2.jd $$\chi_{6384}(563, \cdot)$$ n/a 5088 4
6384.2.jf $$\chi_{6384}(331, \cdot)$$ n/a 2560 4
6384.2.ji $$\chi_{6384}(1109, \cdot)$$ n/a 5088 4
6384.2.jj $$\chi_{6384}(271, \cdot)$$ n/a 960 6
6384.2.jl $$\chi_{6384}(409, \cdot)$$ None 0 6
6384.2.jo $$\chi_{6384}(25, \cdot)$$ None 0 6
6384.2.jq $$\chi_{6384}(79, \cdot)$$ n/a 960 6
6384.2.jr $$\chi_{6384}(1895, \cdot)$$ None 0 6
6384.2.jt $$\chi_{6384}(929, \cdot)$$ n/a 1896 6
6384.2.jw $$\chi_{6384}(401, \cdot)$$ n/a 1896 6
6384.2.jy $$\chi_{6384}(359, \cdot)$$ None 0 6
6384.2.jz $$\chi_{6384}(1871, \cdot)$$ n/a 1920 6
6384.2.kb $$\chi_{6384}(1913, \cdot)$$ None 0 6
6384.2.ke $$\chi_{6384}(2201, \cdot)$$ None 0 6
6384.2.kg $$\chi_{6384}(1055, \cdot)$$ n/a 1920 6
6384.2.ki $$\chi_{6384}(55, \cdot)$$ None 0 6
6384.2.kk $$\chi_{6384}(97, \cdot)$$ n/a 960 6
6384.2.km $$\chi_{6384}(295, \cdot)$$ None 0 6
6384.2.kp $$\chi_{6384}(1343, \cdot)$$ n/a 1920 6
6384.2.kr $$\chi_{6384}(377, \cdot)$$ None 0 6
6384.2.ks $$\chi_{6384}(281, \cdot)$$ None 0 6
6384.2.ku $$\chi_{6384}(575, \cdot)$$ n/a 1440 6
6384.2.kw $$\chi_{6384}(583, \cdot)$$ None 0 6
6384.2.la $$\chi_{6384}(1153, \cdot)$$ n/a 960 6
6384.2.lc $$\chi_{6384}(871, \cdot)$$ None 0 6
6384.2.ld $$\chi_{6384}(17, \cdot)$$ n/a 1896 6
6384.2.lf $$\chi_{6384}(887, \cdot)$$ None 0 6
6384.2.li $$\chi_{6384}(23, \cdot)$$ None 0 6
6384.2.lk $$\chi_{6384}(641, \cdot)$$ n/a 1896 6
6384.2.lm $$\chi_{6384}(169, \cdot)$$ None 0 6
6384.2.lo $$\chi_{6384}(127, \cdot)$$ n/a 720 6
6384.2.lp $$\chi_{6384}(1567, \cdot)$$ n/a 960 6
6384.2.lr $$\chi_{6384}(1609, \cdot)$$ None 0 6
6384.2.lu $$\chi_{6384}(1457, \cdot)$$ n/a 1440 6
6384.2.lw $$\chi_{6384}(1415, \cdot)$$ None 0 6
6384.2.lx $$\chi_{6384}(167, \cdot)$$ None 0 6
6384.2.lz $$\chi_{6384}(2897, \cdot)$$ n/a 1896 6
6384.2.mb $$\chi_{6384}(1321, \cdot)$$ None 0 6
6384.2.md $$\chi_{6384}(1279, \cdot)$$ n/a 960 6
6384.2.mg $$\chi_{6384}(751, \cdot)$$ n/a 960 6
6384.2.mi $$\chi_{6384}(2137, \cdot)$$ None 0 6
6384.2.mk $$\chi_{6384}(1495, \cdot)$$ None 0 6
6384.2.mn $$\chi_{6384}(199, \cdot)$$ None 0 6
6384.2.mp $$\chi_{6384}(241, \cdot)$$ n/a 960 6
6384.2.mq $$\chi_{6384}(2825, \cdot)$$ None 0 6
6384.2.ms $$\chi_{6384}(2543, \cdot)$$ n/a 1920 6
6384.2.mv $$\chi_{6384}(143, \cdot)$$ n/a 1920 6
6384.2.mx $$\chi_{6384}(1529, \cdot)$$ None 0 6
6384.2.my $$\chi_{6384}(275, \cdot)$$ n/a 15264 12
6384.2.nb $$\chi_{6384}(605, \cdot)$$ n/a 15264 12
6384.2.nd $$\chi_{6384}(59, \cdot)$$ n/a 15264 12
6384.2.ne $$\chi_{6384}(317, \cdot)$$ n/a 15264 12
6384.2.ng $$\chi_{6384}(187, \cdot)$$ n/a 7680 12
6384.2.nj $$\chi_{6384}(1213, \cdot)$$ n/a 7680 12
6384.2.nk $$\chi_{6384}(85, \cdot)$$ n/a 5760 12
6384.2.nn $$\chi_{6384}(139, \cdot)$$ n/a 7680 12
6384.2.np $$\chi_{6384}(67, \cdot)$$ n/a 7680 12
6384.2.nq $$\chi_{6384}(565, \cdot)$$ n/a 7680 12
6384.2.nt $$\chi_{6384}(13, \cdot)$$ n/a 7680 12
6384.2.nu $$\chi_{6384}(211, \cdot)$$ n/a 5760 12
6384.2.nw $$\chi_{6384}(53, \cdot)$$ n/a 15264 12
6384.2.nz $$\chi_{6384}(299, \cdot)$$ n/a 15264 12
6384.2.oa $$\chi_{6384}(755, \cdot)$$ n/a 15264 12
6384.2.od $$\chi_{6384}(29, \cdot)$$ n/a 11520 12
6384.2.of $$\chi_{6384}(5, \cdot)$$ n/a 15264 12
6384.2.og $$\chi_{6384}(947, \cdot)$$ n/a 15264 12
6384.2.oj $$\chi_{6384}(491, \cdot)$$ n/a 11520 12
6384.2.ok $$\chi_{6384}(461, \cdot)$$ n/a 15264 12
6384.2.om $$\chi_{6384}(325, \cdot)$$ n/a 7680 12
6384.2.op $$\chi_{6384}(907, \cdot)$$ n/a 7680 12
6384.2.or $$\chi_{6384}(541, \cdot)$$ n/a 7680 12
6384.2.os $$\chi_{6384}(283, \cdot)$$ n/a 7680 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6384))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6384)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1064))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1596))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2128))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3192))$$$$^{\oplus 2}$$