Properties

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

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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

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