# Properties

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

## 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

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