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Properties

Label 8379.2
Level 8379
Weight 2
Dimension 1911594
Nonzero newspaces 184
Sturm bound 10160640

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Defining parameters

Level: \( N \) = \( 8379 = 3^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 184 \)
Sturm bound: \(10160640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8379))\).

Total New Old
Modular forms 2557440 1926434 631006
Cusp forms 2522881 1911594 611287
Eisenstein series 34559 14840 19719

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8379))\)

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
8379.2.a \(\chi_{8379}(1, \cdot)\) 8379.2.a.a 1 1
8379.2.a.b 1
8379.2.a.c 1
8379.2.a.d 1
8379.2.a.e 1
8379.2.a.f 1
8379.2.a.g 1
8379.2.a.h 1
8379.2.a.i 1
8379.2.a.j 1
8379.2.a.k 1
8379.2.a.l 1
8379.2.a.m 1
8379.2.a.n 1
8379.2.a.o 1
8379.2.a.p 1
8379.2.a.q 1
8379.2.a.r 2
8379.2.a.s 2
8379.2.a.t 2
8379.2.a.u 2
8379.2.a.v 2
8379.2.a.w 2
8379.2.a.x 2
8379.2.a.y 2
8379.2.a.z 2
8379.2.a.ba 2
8379.2.a.bb 2
8379.2.a.bc 2
8379.2.a.bd 2
8379.2.a.be 2
8379.2.a.bf 2
8379.2.a.bg 2
8379.2.a.bh 2
8379.2.a.bi 2
8379.2.a.bj 2
8379.2.a.bk 2
8379.2.a.bl 2
8379.2.a.bm 2
8379.2.a.bn 2
8379.2.a.bo 3
8379.2.a.bp 3
8379.2.a.bq 3
8379.2.a.br 4
8379.2.a.bs 4
8379.2.a.bt 4
8379.2.a.bu 4
8379.2.a.bv 4
8379.2.a.bw 4
8379.2.a.bx 4
8379.2.a.by 4
8379.2.a.bz 4
8379.2.a.ca 4
8379.2.a.cb 5
8379.2.a.cc 5
8379.2.a.cd 5
8379.2.a.ce 5
8379.2.a.cf 6
8379.2.a.cg 6
8379.2.a.ch 6
8379.2.a.ci 6
8379.2.a.cj 6
8379.2.a.ck 7
8379.2.a.cl 7
8379.2.a.cm 8
8379.2.a.cn 8
8379.2.a.co 8
8379.2.a.cp 8
8379.2.a.cq 8
8379.2.a.cr 8
8379.2.a.cs 10
8379.2.a.ct 10
8379.2.a.cu 12
8379.2.a.cv 12
8379.2.a.cw 20
8379.2.a.cx 20
8379.2.c \(\chi_{8379}(4654, \cdot)\) n/a 328 1
8379.2.d \(\chi_{8379}(4409, \cdot)\) n/a 240 1
8379.2.f \(\chi_{8379}(7694, \cdot)\) n/a 272 1
8379.2.i \(\chi_{8379}(3754, \cdot)\) n/a 660 2
8379.2.j \(\chi_{8379}(2566, \cdot)\) n/a 600 2
8379.2.k \(\chi_{8379}(4852, \cdot)\) n/a 672 2
8379.2.l \(\chi_{8379}(5065, \cdot)\) n/a 1584 2
8379.2.m \(\chi_{8379}(2794, \cdot)\) n/a 1476 2
8379.2.n \(\chi_{8379}(520, \cdot)\) n/a 1584 2
8379.2.o \(\chi_{8379}(2500, \cdot)\) n/a 1620 2
8379.2.p \(\chi_{8379}(4624, \cdot)\) n/a 1584 2
8379.2.q \(\chi_{8379}(4048, \cdot)\) n/a 1440 2
8379.2.r \(\chi_{8379}(1255, \cdot)\) n/a 1440 2
8379.2.s \(\chi_{8379}(2059, \cdot)\) n/a 1620 2
8379.2.t \(\chi_{8379}(961, \cdot)\) n/a 1584 2
8379.2.u \(\chi_{8379}(3313, \cdot)\) n/a 660 2
8379.2.v \(\chi_{8379}(1342, \cdot)\) n/a 660 2
8379.2.x \(\chi_{8379}(3902, \cdot)\) n/a 1584 2
8379.2.ba \(\chi_{8379}(3674, \cdot)\) n/a 1584 2
8379.2.bb \(\chi_{8379}(3155, \cdot)\) n/a 1440 2
8379.2.be \(\chi_{8379}(607, \cdot)\) n/a 1584 2
8379.2.bf \(\chi_{8379}(2155, \cdot)\) n/a 1584 2
8379.2.bi \(\chi_{8379}(31, \cdot)\) n/a 1584 2
8379.2.bk \(\chi_{8379}(2420, \cdot)\) n/a 536 2
8379.2.bl \(\chi_{8379}(569, \cdot)\) n/a 1584 2
8379.2.bo \(\chi_{8379}(6449, \cdot)\) n/a 1584 2
8379.2.bp \(\chi_{8379}(50, \cdot)\) n/a 1620 2
8379.2.bx \(\chi_{8379}(2174, \cdot)\) n/a 1584 2
8379.2.ca \(\chi_{8379}(2108, \cdot)\) n/a 1620 2
8379.2.cb \(\chi_{8379}(6890, \cdot)\) n/a 1584 2
8379.2.cd \(\chi_{8379}(2402, \cdot)\) n/a 544 2
8379.2.cg \(\chi_{8379}(1880, \cdot)\) n/a 536 2
8379.2.ch \(\chi_{8379}(863, \cdot)\) n/a 536 2
8379.2.cn \(\chi_{8379}(2596, \cdot)\) n/a 1584 2
8379.2.co \(\chi_{8379}(2824, \cdot)\) n/a 1584 2
8379.2.cr \(\chi_{8379}(3400, \cdot)\) n/a 1584 2
8379.2.cs \(\chi_{8379}(4343, \cdot)\) n/a 1584 2
8379.2.cv \(\chi_{8379}(1550, \cdot)\) n/a 1584 2
8379.2.cw \(\chi_{8379}(1616, \cdot)\) n/a 1440 2
8379.2.cy \(\chi_{8379}(881, \cdot)\) n/a 528 2
8379.2.db \(\chi_{8379}(1844, \cdot)\) n/a 480 2
8379.2.dc \(\chi_{8379}(2861, \cdot)\) n/a 536 2
8379.2.df \(\chi_{8379}(901, \cdot)\) n/a 660 2
8379.2.dg \(\chi_{8379}(2089, \cdot)\) n/a 660 2
8379.2.dj \(\chi_{8379}(7741, \cdot)\) n/a 656 2
8379.2.dl \(\chi_{8379}(1861, \cdot)\) n/a 1584 2
8379.2.dm \(\chi_{8379}(2383, \cdot)\) n/a 1584 2
8379.2.dp \(\chi_{8379}(6928, \cdot)\) n/a 1584 2
8379.2.dq \(\chi_{8379}(362, \cdot)\) n/a 1440 2
8379.2.dt \(\chi_{8379}(68, \cdot)\) n/a 1584 2
8379.2.du \(\chi_{8379}(4115, \cdot)\) n/a 1584 2
8379.2.dx \(\chi_{8379}(1304, \cdot)\) n/a 536 2
8379.2.eb \(\chi_{8379}(2615, \cdot)\) n/a 1584 2
8379.2.ee \(\chi_{8379}(5636, \cdot)\) n/a 1620 2
8379.2.ef \(\chi_{8379}(3362, \cdot)\) n/a 1584 2
8379.2.ei \(\chi_{8379}(1198, \cdot)\) n/a 2520 6
8379.2.ej \(\chi_{8379}(2284, \cdot)\) n/a 4752 6
8379.2.ek \(\chi_{8379}(1030, \cdot)\) n/a 4860 6
8379.2.el \(\chi_{8379}(655, \cdot)\) n/a 4752 6
8379.2.em \(\chi_{8379}(3595, \cdot)\) n/a 4752 6
8379.2.en \(\chi_{8379}(442, \cdot)\) n/a 2022 6
8379.2.eo \(\chi_{8379}(1108, \cdot)\) n/a 1974 6
8379.2.ep \(\chi_{8379}(214, \cdot)\) n/a 4752 6
8379.2.eq \(\chi_{8379}(2353, \cdot)\) n/a 4860 6
8379.2.er \(\chi_{8379}(226, \cdot)\) n/a 1974 6
8379.2.eu \(\chi_{8379}(512, \cdot)\) n/a 2256 6
8379.2.ew \(\chi_{8379}(818, \cdot)\) n/a 2016 6
8379.2.ex \(\chi_{8379}(1063, \cdot)\) n/a 2796 6
8379.2.ez \(\chi_{8379}(998, \cdot)\) n/a 1596 6
8379.2.fc \(\chi_{8379}(1226, \cdot)\) n/a 4860 6
8379.2.fd \(\chi_{8379}(716, \cdot)\) n/a 4752 6
8379.2.fl \(\chi_{8379}(116, \cdot)\) n/a 1596 6
8379.2.fm \(\chi_{8379}(1079, \cdot)\) n/a 1644 6
8379.2.fr \(\chi_{8379}(128, \cdot)\) n/a 4752 6
8379.2.fs \(\chi_{8379}(1598, \cdot)\) n/a 4752 6
8379.2.ft \(\chi_{8379}(344, \cdot)\) n/a 4860 6
8379.2.fu \(\chi_{8379}(2333, \cdot)\) n/a 4752 6
8379.2.gb \(\chi_{8379}(1175, \cdot)\) n/a 4752 6
8379.2.gc \(\chi_{8379}(1391, \cdot)\) n/a 4752 6
8379.2.gf \(\chi_{8379}(80, \cdot)\) n/a 1596 6
8379.2.gg \(\chi_{8379}(2008, \cdot)\) n/a 1980 6
8379.2.gh \(\chi_{8379}(325, \cdot)\) n/a 1974 6
8379.2.gm \(\chi_{8379}(166, \cdot)\) n/a 4752 6
8379.2.gn \(\chi_{8379}(1636, \cdot)\) n/a 4752 6
8379.2.go \(\chi_{8379}(97, \cdot)\) n/a 4752 6
8379.2.gp \(\chi_{8379}(754, \cdot)\) n/a 4752 6
8379.2.gu \(\chi_{8379}(815, \cdot)\) n/a 4752 6
8379.2.gv \(\chi_{8379}(587, \cdot)\) n/a 4752 6
8379.2.gw \(\chi_{8379}(803, \cdot)\) n/a 4752 6
8379.2.gx \(\chi_{8379}(2714, \cdot)\) n/a 4752 6
8379.2.hc \(\chi_{8379}(215, \cdot)\) n/a 1596 6
8379.2.hd \(\chi_{8379}(2645, \cdot)\) n/a 1608 6
8379.2.he \(\chi_{8379}(1207, \cdot)\) n/a 1974 6
8379.2.hh \(\chi_{8379}(2371, \cdot)\) n/a 4752 6
8379.2.hi \(\chi_{8379}(979, \cdot)\) n/a 4752 6
8379.2.hk \(\chi_{8379}(676, \cdot)\) n/a 5568 12
8379.2.hl \(\chi_{8379}(634, \cdot)\) n/a 13392 12
8379.2.hm \(\chi_{8379}(862, \cdot)\) n/a 13392 12
8379.2.hn \(\chi_{8379}(58, \cdot)\) n/a 12096 12
8379.2.ho \(\chi_{8379}(457, \cdot)\) n/a 12096 12
8379.2.hp \(\chi_{8379}(562, \cdot)\) n/a 13392 12
8379.2.hq \(\chi_{8379}(106, \cdot)\) n/a 13392 12
8379.2.hr \(\chi_{8379}(1075, \cdot)\) n/a 13392 12
8379.2.hs \(\chi_{8379}(400, \cdot)\) n/a 12096 12
8379.2.ht \(\chi_{8379}(121, \cdot)\) n/a 13392 12
8379.2.hu \(\chi_{8379}(64, \cdot)\) n/a 5592 12
8379.2.hv \(\chi_{8379}(172, \cdot)\) n/a 5040 12
8379.2.hw \(\chi_{8379}(163, \cdot)\) n/a 5568 12
8379.2.hz \(\chi_{8379}(968, \cdot)\) n/a 13392 12
8379.2.ia \(\chi_{8379}(806, \cdot)\) n/a 13392 12
8379.2.id \(\chi_{8379}(65, \cdot)\) n/a 13392 12
8379.2.ih \(\chi_{8379}(107, \cdot)\) n/a 4464 12
8379.2.ik \(\chi_{8379}(482, \cdot)\) n/a 13392 12
8379.2.il \(\chi_{8379}(1265, \cdot)\) n/a 13392 12
8379.2.io \(\chi_{8379}(248, \cdot)\) n/a 12096 12
8379.2.ip \(\chi_{8379}(787, \cdot)\) n/a 13392 12
8379.2.is \(\chi_{8379}(544, \cdot)\) n/a 13392 12
8379.2.it \(\chi_{8379}(265, \cdot)\) n/a 13392 12
8379.2.iv \(\chi_{8379}(559, \cdot)\) n/a 5592 12
8379.2.iy \(\chi_{8379}(208, \cdot)\) n/a 5568 12
8379.2.iz \(\chi_{8379}(829, \cdot)\) n/a 5568 12
8379.2.jc \(\chi_{8379}(467, \cdot)\) n/a 4464 12
8379.2.jd \(\chi_{8379}(647, \cdot)\) n/a 4032 12
8379.2.jg \(\chi_{8379}(125, \cdot)\) n/a 4512 12
8379.2.ji \(\chi_{8379}(20, \cdot)\) n/a 12096 12
8379.2.jj \(\chi_{8379}(353, \cdot)\) n/a 13392 12
8379.2.jm \(\chi_{8379}(425, \cdot)\) n/a 13392 12
8379.2.jn \(\chi_{8379}(94, \cdot)\) n/a 13392 12
8379.2.jq \(\chi_{8379}(103, \cdot)\) n/a 13392 12
8379.2.jr \(\chi_{8379}(160, \cdot)\) n/a 13392 12
8379.2.jx \(\chi_{8379}(620, \cdot)\) n/a 4464 12
8379.2.jy \(\chi_{8379}(170, \cdot)\) n/a 4464 12
8379.2.kb \(\chi_{8379}(8, \cdot)\) n/a 4512 12
8379.2.kd \(\chi_{8379}(578, \cdot)\) n/a 13392 12
8379.2.ke \(\chi_{8379}(113, \cdot)\) n/a 13392 12
8379.2.kh \(\chi_{8379}(506, \cdot)\) n/a 13392 12
8379.2.kp \(\chi_{8379}(407, \cdot)\) n/a 13392 12
8379.2.kq \(\chi_{8379}(464, \cdot)\) n/a 13392 12
8379.2.kt \(\chi_{8379}(284, \cdot)\) n/a 13392 12
8379.2.ku \(\chi_{8379}(26, \cdot)\) n/a 4464 12
8379.2.kw \(\chi_{8379}(502, \cdot)\) n/a 13392 12
8379.2.kz \(\chi_{8379}(601, \cdot)\) n/a 13392 12
8379.2.la \(\chi_{8379}(493, \cdot)\) n/a 13392 12
8379.2.ld \(\chi_{8379}(761, \cdot)\) n/a 12096 12
8379.2.le \(\chi_{8379}(83, \cdot)\) n/a 13392 12
8379.2.lh \(\chi_{8379}(311, \cdot)\) n/a 13392 12
8379.2.lj \(\chi_{8379}(145, \cdot)\) n/a 5568 12
8379.2.lk \(\chi_{8379}(100, \cdot)\) n/a 16740 36
8379.2.ll \(\chi_{8379}(310, \cdot)\) n/a 40176 36
8379.2.lm \(\chi_{8379}(232, \cdot)\) n/a 40176 36
8379.2.ln \(\chi_{8379}(253, \cdot)\) n/a 16704 36
8379.2.lo \(\chi_{8379}(289, \cdot)\) n/a 16740 36
8379.2.lp \(\chi_{8379}(25, \cdot)\) n/a 40176 36
8379.2.lq \(\chi_{8379}(4, \cdot)\) n/a 40176 36
8379.2.lr \(\chi_{8379}(43, \cdot)\) n/a 40176 36
8379.2.ls \(\chi_{8379}(130, \cdot)\) n/a 40176 36
8379.2.lu \(\chi_{8379}(52, \cdot)\) n/a 40176 36
8379.2.lv \(\chi_{8379}(34, \cdot)\) n/a 40176 36
8379.2.ly \(\chi_{8379}(10, \cdot)\) n/a 16740 36
8379.2.lz \(\chi_{8379}(17, \cdot)\) n/a 13464 36
8379.2.ma \(\chi_{8379}(62, \cdot)\) n/a 13392 36
8379.2.mf \(\chi_{8379}(500, \cdot)\) n/a 40176 36
8379.2.mg \(\chi_{8379}(5, \cdot)\) n/a 40176 36
8379.2.mh \(\chi_{8379}(104, \cdot)\) n/a 40176 36
8379.2.mi \(\chi_{8379}(47, \cdot)\) n/a 40176 36
8379.2.mn \(\chi_{8379}(124, \cdot)\) n/a 40176 36
8379.2.mo \(\chi_{8379}(13, \cdot)\) n/a 40176 36
8379.2.mp \(\chi_{8379}(40, \cdot)\) n/a 40176 36
8379.2.mq \(\chi_{8379}(250, \cdot)\) n/a 40176 36
8379.2.mv \(\chi_{8379}(181, \cdot)\) n/a 16704 36
8379.2.mw \(\chi_{8379}(136, \cdot)\) n/a 16740 36
8379.2.mx \(\chi_{8379}(332, \cdot)\) n/a 13464 36
8379.2.na \(\chi_{8379}(272, \cdot)\) n/a 40176 36
8379.2.nb \(\chi_{8379}(194, \cdot)\) n/a 40176 36
8379.2.ni \(\chi_{8379}(317, \cdot)\) n/a 40176 36
8379.2.nj \(\chi_{8379}(155, \cdot)\) n/a 40176 36
8379.2.nk \(\chi_{8379}(2, \cdot)\) n/a 40176 36
8379.2.nl \(\chi_{8379}(200, \cdot)\) n/a 40176 36
8379.2.nq \(\chi_{8379}(242, \cdot)\) n/a 13464 36
8379.2.nr \(\chi_{8379}(71, \cdot)\) n/a 13392 36
8379.2.nz \(\chi_{8379}(29, \cdot)\) n/a 40176 36
8379.2.oa \(\chi_{8379}(86, \cdot)\) n/a 40176 36
8379.2.od \(\chi_{8379}(53, \cdot)\) n/a 13464 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8379))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8379)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1197))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2793))\)\(^{\oplus 2}\)