Properties

 Label 4080.2 Level 4080 Weight 2 Dimension 169076 Nonzero newspaces 100 Sturm bound 1769472

Defining parameters

 Level: $$N$$ = $$4080 = 2^{4} \cdot 3 \cdot 5 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$1769472$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4080))$$.

Total New Old
Modular forms 449536 170692 278844
Cusp forms 435201 169076 266125
Eisenstein series 14335 1616 12719

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4080))$$

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
4080.2.a $$\chi_{4080}(1, \cdot)$$ 4080.2.a.a 1 1
4080.2.a.b 1
4080.2.a.c 1
4080.2.a.d 1
4080.2.a.e 1
4080.2.a.f 1
4080.2.a.g 1
4080.2.a.h 1
4080.2.a.i 1
4080.2.a.j 1
4080.2.a.k 1
4080.2.a.l 1
4080.2.a.m 1
4080.2.a.n 1
4080.2.a.o 1
4080.2.a.p 1
4080.2.a.q 1
4080.2.a.r 1
4080.2.a.s 1
4080.2.a.t 1
4080.2.a.u 1
4080.2.a.v 1
4080.2.a.w 1
4080.2.a.x 1
4080.2.a.y 1
4080.2.a.z 1
4080.2.a.ba 1
4080.2.a.bb 1
4080.2.a.bc 1
4080.2.a.bd 1
4080.2.a.be 1
4080.2.a.bf 1
4080.2.a.bg 2
4080.2.a.bh 2
4080.2.a.bi 2
4080.2.a.bj 2
4080.2.a.bk 2
4080.2.a.bl 2
4080.2.a.bm 2
4080.2.a.bn 2
4080.2.a.bo 2
4080.2.a.bp 2
4080.2.a.bq 2
4080.2.a.br 3
4080.2.a.bs 3
4080.2.a.bt 4
4080.2.c $$\chi_{4080}(4079, \cdot)$$ n/a 216 1
4080.2.e $$\chi_{4080}(3911, \cdot)$$ None 0 1
4080.2.f $$\chi_{4080}(409, \cdot)$$ None 0 1
4080.2.h $$\chi_{4080}(3841, \cdot)$$ 4080.2.h.a 2 1
4080.2.h.b 2
4080.2.h.c 2
4080.2.h.d 2
4080.2.h.e 2
4080.2.h.f 2
4080.2.h.g 2
4080.2.h.h 2
4080.2.h.i 2
4080.2.h.j 2
4080.2.h.k 4
4080.2.h.l 4
4080.2.h.m 4
4080.2.h.n 4
4080.2.h.o 4
4080.2.h.p 4
4080.2.h.q 4
4080.2.h.r 6
4080.2.h.s 8
4080.2.h.t 10
4080.2.k $$\chi_{4080}(1801, \cdot)$$ None 0 1
4080.2.m $$\chi_{4080}(2449, \cdot)$$ 4080.2.m.a 2 1
4080.2.m.b 2
4080.2.m.c 2
4080.2.m.d 2
4080.2.m.e 2
4080.2.m.f 2
4080.2.m.g 2
4080.2.m.h 2
4080.2.m.i 2
4080.2.m.j 2
4080.2.m.k 2
4080.2.m.l 2
4080.2.m.m 4
4080.2.m.n 4
4080.2.m.o 4
4080.2.m.p 6
4080.2.m.q 10
4080.2.m.r 10
4080.2.m.s 10
4080.2.m.t 12
4080.2.m.u 12
4080.2.n $$\chi_{4080}(1871, \cdot)$$ n/a 128 1
4080.2.p $$\chi_{4080}(2039, \cdot)$$ None 0 1
4080.2.r $$\chi_{4080}(2041, \cdot)$$ None 0 1
4080.2.t $$\chi_{4080}(2209, \cdot)$$ n/a 108 1
4080.2.w $$\chi_{4080}(1631, \cdot)$$ n/a 144 1
4080.2.y $$\chi_{4080}(2279, \cdot)$$ None 0 1
4080.2.z $$\chi_{4080}(239, \cdot)$$ n/a 192 1
4080.2.bb $$\chi_{4080}(3671, \cdot)$$ None 0 1
4080.2.be $$\chi_{4080}(169, \cdot)$$ None 0 1
4080.2.bh $$\chi_{4080}(2333, \cdot)$$ n/a 1712 2
4080.2.bi $$\chi_{4080}(523, \cdot)$$ n/a 864 2
4080.2.bk $$\chi_{4080}(2393, \cdot)$$ None 0 2
4080.2.bn $$\chi_{4080}(463, \cdot)$$ n/a 216 2
4080.2.bp $$\chi_{4080}(1189, \cdot)$$ n/a 864 2
4080.2.bq $$\chi_{4080}(1021, \cdot)$$ n/a 512 2
4080.2.bt $$\chi_{4080}(1259, \cdot)$$ n/a 1536 2
4080.2.bu $$\chi_{4080}(611, \cdot)$$ n/a 1152 2
4080.2.bw $$\chi_{4080}(353, \cdot)$$ n/a 424 2
4080.2.bz $$\chi_{4080}(727, \cdot)$$ None 0 2
4080.2.cb $$\chi_{4080}(667, \cdot)$$ n/a 864 2
4080.2.cc $$\chi_{4080}(293, \cdot)$$ n/a 1712 2
4080.2.cf $$\chi_{4080}(3127, \cdot)$$ None 0 2
4080.2.ch $$\chi_{4080}(2177, \cdot)$$ n/a 384 2
4080.2.cj $$\chi_{4080}(829, \cdot)$$ n/a 864 2
4080.2.cl $$\chi_{4080}(1381, \cdot)$$ n/a 576 2
4080.2.cn $$\chi_{4080}(659, \cdot)$$ n/a 1712 2
4080.2.cp $$\chi_{4080}(1211, \cdot)$$ n/a 1152 2
4080.2.cq $$\chi_{4080}(1327, \cdot)$$ n/a 192 2
4080.2.cs $$\chi_{4080}(713, \cdot)$$ None 0 2
4080.2.cv $$\chi_{4080}(1271, \cdot)$$ None 0 2
4080.2.cw $$\chi_{4080}(769, \cdot)$$ n/a 216 2
4080.2.cy $$\chi_{4080}(1123, \cdot)$$ n/a 768 2
4080.2.da $$\chi_{4080}(917, \cdot)$$ n/a 1712 2
4080.2.dd $$\chi_{4080}(1157, \cdot)$$ n/a 1536 2
4080.2.df $$\chi_{4080}(883, \cdot)$$ n/a 864 2
4080.2.dg $$\chi_{4080}(1679, \cdot)$$ n/a 432 2
4080.2.dj $$\chi_{4080}(361, \cdot)$$ None 0 2
4080.2.dl $$\chi_{4080}(1441, \cdot)$$ n/a 144 2
4080.2.dm $$\chi_{4080}(599, \cdot)$$ None 0 2
4080.2.do $$\chi_{4080}(1733, \cdot)$$ n/a 1712 2
4080.2.dq $$\chi_{4080}(307, \cdot)$$ n/a 768 2
4080.2.dt $$\chi_{4080}(67, \cdot)$$ n/a 864 2
4080.2.dv $$\chi_{4080}(1973, \cdot)$$ n/a 1536 2
4080.2.dw $$\chi_{4080}(1849, \cdot)$$ None 0 2
4080.2.dz $$\chi_{4080}(191, \cdot)$$ n/a 288 2
4080.2.ea $$\chi_{4080}(1937, \cdot)$$ n/a 424 2
4080.2.ec $$\chi_{4080}(103, \cdot)$$ None 0 2
4080.2.ee $$\chi_{4080}(251, \cdot)$$ n/a 1152 2
4080.2.eg $$\chi_{4080}(1619, \cdot)$$ n/a 1712 2
4080.2.ei $$\chi_{4080}(421, \cdot)$$ n/a 576 2
4080.2.ek $$\chi_{4080}(1789, \cdot)$$ n/a 864 2
4080.2.en $$\chi_{4080}(137, \cdot)$$ None 0 2
4080.2.ep $$\chi_{4080}(1087, \cdot)$$ n/a 216 2
4080.2.eq $$\chi_{4080}(3523, \cdot)$$ n/a 864 2
4080.2.et $$\chi_{4080}(1517, \cdot)$$ n/a 1712 2
4080.2.eu $$\chi_{4080}(3583, \cdot)$$ n/a 216 2
4080.2.ex $$\chi_{4080}(1577, \cdot)$$ None 0 2
4080.2.ez $$\chi_{4080}(851, \cdot)$$ n/a 1024 2
4080.2.fa $$\chi_{4080}(1019, \cdot)$$ n/a 1712 2
4080.2.fd $$\chi_{4080}(781, \cdot)$$ n/a 576 2
4080.2.fe $$\chi_{4080}(1429, \cdot)$$ n/a 768 2
4080.2.fg $$\chi_{4080}(1543, \cdot)$$ None 0 2
4080.2.fj $$\chi_{4080}(1313, \cdot)$$ n/a 424 2
4080.2.fk $$\chi_{4080}(1373, \cdot)$$ n/a 1712 2
4080.2.fn $$\chi_{4080}(1483, \cdot)$$ n/a 864 2
4080.2.fp $$\chi_{4080}(43, \cdot)$$ n/a 1728 4
4080.2.fq $$\chi_{4080}(53, \cdot)$$ n/a 3424 4
4080.2.ft $$\chi_{4080}(671, \cdot)$$ n/a 576 4
4080.2.fu $$\chi_{4080}(961, \cdot)$$ n/a 288 4
4080.2.fx $$\chi_{4080}(359, \cdot)$$ None 0 4
4080.2.fy $$\chi_{4080}(1369, \cdot)$$ None 0 4
4080.2.ga $$\chi_{4080}(773, \cdot)$$ n/a 3424 4
4080.2.gd $$\chi_{4080}(763, \cdot)$$ n/a 1728 4
4080.2.ge $$\chi_{4080}(1861, \cdot)$$ n/a 1152 4
4080.2.gf $$\chi_{4080}(491, \cdot)$$ n/a 2304 4
4080.2.gk $$\chi_{4080}(229, \cdot)$$ n/a 1728 4
4080.2.gl $$\chi_{4080}(179, \cdot)$$ n/a 3424 4
4080.2.gm $$\chi_{4080}(257, \cdot)$$ n/a 848 4
4080.2.gn $$\chi_{4080}(1097, \cdot)$$ None 0 4
4080.2.go $$\chi_{4080}(967, \cdot)$$ None 0 4
4080.2.gp $$\chi_{4080}(127, \cdot)$$ n/a 432 4
4080.2.gy $$\chi_{4080}(247, \cdot)$$ None 0 4
4080.2.gz $$\chi_{4080}(943, \cdot)$$ n/a 432 4
4080.2.ha $$\chi_{4080}(593, \cdot)$$ n/a 848 4
4080.2.hb $$\chi_{4080}(1817, \cdot)$$ None 0 4
4080.2.he $$\chi_{4080}(59, \cdot)$$ n/a 3424 4
4080.2.hf $$\chi_{4080}(349, \cdot)$$ n/a 1728 4
4080.2.hg $$\chi_{4080}(1691, \cdot)$$ n/a 2304 4
4080.2.hh $$\chi_{4080}(661, \cdot)$$ n/a 1152 4
4080.2.hk $$\chi_{4080}(1147, \cdot)$$ n/a 1728 4
4080.2.hn $$\chi_{4080}(893, \cdot)$$ n/a 3424 4
4080.2.ho $$\chi_{4080}(121, \cdot)$$ None 0 4
4080.2.hr $$\chi_{4080}(791, \cdot)$$ None 0 4
4080.2.hs $$\chi_{4080}(49, \cdot)$$ n/a 432 4
4080.2.hv $$\chi_{4080}(1199, \cdot)$$ n/a 864 4
4080.2.hx $$\chi_{4080}(1613, \cdot)$$ n/a 3424 4
4080.2.hy $$\chi_{4080}(427, \cdot)$$ n/a 1728 4
4080.2.ia $$\chi_{4080}(23, \cdot)$$ None 0 8
4080.2.ic $$\chi_{4080}(313, \cdot)$$ None 0 8
4080.2.ig $$\chi_{4080}(1061, \cdot)$$ n/a 4608 8
4080.2.ih $$\chi_{4080}(139, \cdot)$$ n/a 3456 8
4080.2.ii $$\chi_{4080}(91, \cdot)$$ n/a 2304 8
4080.2.ij $$\chi_{4080}(1469, \cdot)$$ n/a 6848 8
4080.2.in $$\chi_{4080}(913, \cdot)$$ n/a 864 8
4080.2.ip $$\chi_{4080}(1247, \cdot)$$ n/a 1728 8
4080.2.ir $$\chi_{4080}(37, \cdot)$$ n/a 3456 8
4080.2.it $$\chi_{4080}(947, \cdot)$$ n/a 6848 8
4080.2.iv $$\chi_{4080}(107, \cdot)$$ n/a 6848 8
4080.2.ix $$\chi_{4080}(1117, \cdot)$$ n/a 3456 8
4080.2.iz $$\chi_{4080}(329, \cdot)$$ None 0 8
4080.2.ja $$\chi_{4080}(79, \cdot)$$ n/a 864 8
4080.2.jd $$\chi_{4080}(1111, \cdot)$$ None 0 8
4080.2.je $$\chi_{4080}(401, \cdot)$$ n/a 1152 8
4080.2.jh $$\chi_{4080}(31, \cdot)$$ n/a 576 8
4080.2.ji $$\chi_{4080}(41, \cdot)$$ None 0 8
4080.2.jl $$\chi_{4080}(209, \cdot)$$ n/a 1696 8
4080.2.jm $$\chi_{4080}(199, \cdot)$$ None 0 8
4080.2.jo $$\chi_{4080}(517, \cdot)$$ n/a 3456 8
4080.2.jq $$\chi_{4080}(227, \cdot)$$ n/a 6848 8
4080.2.js $$\chi_{4080}(347, \cdot)$$ n/a 6848 8
4080.2.ju $$\chi_{4080}(133, \cdot)$$ n/a 3456 8
4080.2.jw $$\chi_{4080}(97, \cdot)$$ n/a 864 8
4080.2.jy $$\chi_{4080}(143, \cdot)$$ n/a 1728 8
4080.2.kc $$\chi_{4080}(619, \cdot)$$ n/a 3456 8
4080.2.kd $$\chi_{4080}(581, \cdot)$$ n/a 4608 8
4080.2.ke $$\chi_{4080}(29, \cdot)$$ n/a 6848 8
4080.2.kf $$\chi_{4080}(211, \cdot)$$ n/a 2304 8
4080.2.kj $$\chi_{4080}(743, \cdot)$$ None 0 8
4080.2.kl $$\chi_{4080}(73, \cdot)$$ None 0 8

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4080))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4080)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(255))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(272))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(340))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(408))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(510))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(680))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(816))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1020))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2040))$$$$^{\oplus 2}$$