# Properties

 Label 8280.2 Level 8280 Weight 2 Dimension 739786 Nonzero newspaces 72 Sturm bound 7299072

# Learn more

## Defining parameters

 Level: $$N$$ = $$8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$7299072$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8280))$$.

Total New Old
Modular forms 1841664 744322 1097342
Cusp forms 1807873 739786 1068087
Eisenstein series 33791 4536 29255

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8280))$$

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
8280.2.a $$\chi_{8280}(1, \cdot)$$ 8280.2.a.a 1 1
8280.2.a.b 1
8280.2.a.c 1
8280.2.a.d 1
8280.2.a.e 1
8280.2.a.f 1
8280.2.a.g 1
8280.2.a.h 1
8280.2.a.i 1
8280.2.a.j 1
8280.2.a.k 1
8280.2.a.l 1
8280.2.a.m 1
8280.2.a.n 1
8280.2.a.o 1
8280.2.a.p 1
8280.2.a.q 1
8280.2.a.r 1
8280.2.a.s 1
8280.2.a.t 1
8280.2.a.u 1
8280.2.a.v 1
8280.2.a.w 1
8280.2.a.x 2
8280.2.a.y 2
8280.2.a.z 2
8280.2.a.ba 2
8280.2.a.bb 2
8280.2.a.bc 2
8280.2.a.bd 2
8280.2.a.be 2
8280.2.a.bf 2
8280.2.a.bg 2
8280.2.a.bh 3
8280.2.a.bi 3
8280.2.a.bj 3
8280.2.a.bk 3
8280.2.a.bl 3
8280.2.a.bm 3
8280.2.a.bn 3
8280.2.a.bo 3
8280.2.a.bp 3
8280.2.a.bq 4
8280.2.a.br 5
8280.2.a.bs 5
8280.2.a.bt 6
8280.2.a.bu 6
8280.2.a.bv 7
8280.2.a.bw 7
8280.2.c $$\chi_{8280}(5291, \cdot)$$ n/a 352 1
8280.2.e $$\chi_{8280}(5381, \cdot)$$ n/a 384 1
8280.2.f $$\chi_{8280}(829, \cdot)$$ n/a 660 1
8280.2.h $$\chi_{8280}(5059, \cdot)$$ n/a 716 1
8280.2.k $$\chi_{8280}(4969, \cdot)$$ n/a 164 1
8280.2.m $$\chi_{8280}(919, \cdot)$$ None 0 1
8280.2.n $$\chi_{8280}(1151, \cdot)$$ None 0 1
8280.2.p $$\chi_{8280}(1241, \cdot)$$ 8280.2.p.a 48 1
8280.2.p.b 48
8280.2.r $$\chi_{8280}(91, \cdot)$$ n/a 480 1
8280.2.t $$\chi_{8280}(4141, \cdot)$$ n/a 440 1
8280.2.w $$\chi_{8280}(2069, \cdot)$$ n/a 576 1
8280.2.y $$\chi_{8280}(1979, \cdot)$$ n/a 528 1
8280.2.z $$\chi_{8280}(6209, \cdot)$$ n/a 144 1
8280.2.bb $$\chi_{8280}(6119, \cdot)$$ None 0 1
8280.2.be $$\chi_{8280}(4231, \cdot)$$ None 0 1
8280.2.bg $$\chi_{8280}(2761, \cdot)$$ n/a 528 2
8280.2.bj $$\chi_{8280}(4967, \cdot)$$ None 0 2
8280.2.bk $$\chi_{8280}(737, \cdot)$$ n/a 264 2
8280.2.bl $$\chi_{8280}(3727, \cdot)$$ None 0 2
8280.2.bm $$\chi_{8280}(3817, \cdot)$$ n/a 360 2
8280.2.br $$\chi_{8280}(1243, \cdot)$$ n/a 1320 2
8280.2.bs $$\chi_{8280}(1333, \cdot)$$ n/a 1432 2
8280.2.bt $$\chi_{8280}(827, \cdot)$$ n/a 1152 2
8280.2.bu $$\chi_{8280}(4877, \cdot)$$ n/a 1056 2
8280.2.bx $$\chi_{8280}(1471, \cdot)$$ None 0 2
8280.2.cb $$\chi_{8280}(689, \cdot)$$ n/a 864 2
8280.2.cd $$\chi_{8280}(599, \cdot)$$ None 0 2
8280.2.ce $$\chi_{8280}(4829, \cdot)$$ n/a 3440 2
8280.2.cg $$\chi_{8280}(4739, \cdot)$$ n/a 3168 2
8280.2.cj $$\chi_{8280}(2851, \cdot)$$ n/a 2304 2
8280.2.cl $$\chi_{8280}(1381, \cdot)$$ n/a 2112 2
8280.2.cn $$\chi_{8280}(3911, \cdot)$$ None 0 2
8280.2.cp $$\chi_{8280}(4001, \cdot)$$ n/a 576 2
8280.2.cq $$\chi_{8280}(2209, \cdot)$$ n/a 792 2
8280.2.cs $$\chi_{8280}(3679, \cdot)$$ None 0 2
8280.2.cv $$\chi_{8280}(3589, \cdot)$$ n/a 3168 2
8280.2.cx $$\chi_{8280}(2299, \cdot)$$ n/a 3440 2
8280.2.cy $$\chi_{8280}(2531, \cdot)$$ n/a 2112 2
8280.2.da $$\chi_{8280}(2621, \cdot)$$ n/a 2304 2
8280.2.dc $$\chi_{8280}(361, \cdot)$$ n/a 1200 10
8280.2.dd $$\chi_{8280}(2437, \cdot)$$ n/a 6880 4
8280.2.de $$\chi_{8280}(2347, \cdot)$$ n/a 6336 4
8280.2.dj $$\chi_{8280}(1013, \cdot)$$ n/a 6336 4
8280.2.dk $$\chi_{8280}(3587, \cdot)$$ n/a 6880 4
8280.2.dl $$\chi_{8280}(3497, \cdot)$$ n/a 1584 4
8280.2.dm $$\chi_{8280}(1103, \cdot)$$ None 0 4
8280.2.dr $$\chi_{8280}(1057, \cdot)$$ n/a 1728 4
8280.2.ds $$\chi_{8280}(967, \cdot)$$ None 0 4
8280.2.du $$\chi_{8280}(631, \cdot)$$ None 0 10
8280.2.dx $$\chi_{8280}(719, \cdot)$$ None 0 10
8280.2.dz $$\chi_{8280}(89, \cdot)$$ n/a 1440 10
8280.2.ea $$\chi_{8280}(179, \cdot)$$ n/a 5760 10
8280.2.ec $$\chi_{8280}(1349, \cdot)$$ n/a 5760 10
8280.2.ef $$\chi_{8280}(541, \cdot)$$ n/a 4800 10
8280.2.eh $$\chi_{8280}(451, \cdot)$$ n/a 4800 10
8280.2.ej $$\chi_{8280}(521, \cdot)$$ n/a 960 10
8280.2.el $$\chi_{8280}(71, \cdot)$$ None 0 10
8280.2.em $$\chi_{8280}(199, \cdot)$$ None 0 10
8280.2.eo $$\chi_{8280}(289, \cdot)$$ n/a 1800 10
8280.2.er $$\chi_{8280}(19, \cdot)$$ n/a 7160 10
8280.2.et $$\chi_{8280}(469, \cdot)$$ n/a 7160 10
8280.2.eu $$\chi_{8280}(341, \cdot)$$ n/a 3840 10
8280.2.ew $$\chi_{8280}(611, \cdot)$$ n/a 3840 10
8280.2.ey $$\chi_{8280}(121, \cdot)$$ n/a 5760 20
8280.2.fb $$\chi_{8280}(197, \cdot)$$ n/a 11520 20
8280.2.fc $$\chi_{8280}(107, \cdot)$$ n/a 11520 20
8280.2.fd $$\chi_{8280}(37, \cdot)$$ n/a 14320 20
8280.2.fe $$\chi_{8280}(163, \cdot)$$ n/a 14320 20
8280.2.fj $$\chi_{8280}(217, \cdot)$$ n/a 3600 20
8280.2.fk $$\chi_{8280}(127, \cdot)$$ None 0 20
8280.2.fl $$\chi_{8280}(233, \cdot)$$ n/a 2880 20
8280.2.fm $$\chi_{8280}(143, \cdot)$$ None 0 20
8280.2.fq $$\chi_{8280}(221, \cdot)$$ n/a 23040 20
8280.2.fs $$\chi_{8280}(131, \cdot)$$ n/a 23040 20
8280.2.ft $$\chi_{8280}(619, \cdot)$$ n/a 34400 20
8280.2.fv $$\chi_{8280}(349, \cdot)$$ n/a 34400 20
8280.2.fy $$\chi_{8280}(79, \cdot)$$ None 0 20
8280.2.ga $$\chi_{8280}(49, \cdot)$$ n/a 8640 20
8280.2.gb $$\chi_{8280}(281, \cdot)$$ n/a 5760 20
8280.2.gd $$\chi_{8280}(311, \cdot)$$ None 0 20
8280.2.gf $$\chi_{8280}(301, \cdot)$$ n/a 23040 20
8280.2.gh $$\chi_{8280}(571, \cdot)$$ n/a 23040 20
8280.2.gk $$\chi_{8280}(59, \cdot)$$ n/a 34400 20
8280.2.gm $$\chi_{8280}(149, \cdot)$$ n/a 34400 20
8280.2.gn $$\chi_{8280}(119, \cdot)$$ None 0 20
8280.2.gp $$\chi_{8280}(329, \cdot)$$ n/a 8640 20
8280.2.gt $$\chi_{8280}(511, \cdot)$$ None 0 20
8280.2.gu $$\chi_{8280}(223, \cdot)$$ None 0 40
8280.2.gv $$\chi_{8280}(97, \cdot)$$ n/a 17280 40
8280.2.ha $$\chi_{8280}(263, \cdot)$$ None 0 40
8280.2.hb $$\chi_{8280}(257, \cdot)$$ n/a 17280 40
8280.2.hc $$\chi_{8280}(83, \cdot)$$ n/a 68800 40
8280.2.hd $$\chi_{8280}(77, \cdot)$$ n/a 68800 40
8280.2.hi $$\chi_{8280}(187, \cdot)$$ n/a 68800 40
8280.2.hj $$\chi_{8280}(157, \cdot)$$ n/a 68800 40

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8280))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8280)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(552))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(690))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(828))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(920))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1035))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1380))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1656))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2070))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2760))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4140))$$$$^{\oplus 2}$$