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Properties

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

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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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(6384)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1064))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1596))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6384))\)\(^{\oplus 1}\)