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Properties

Label 5280.2
Level 5280
Weight 2
Dimension 279288
Nonzero newspaces 80
Sturm bound 2949120

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Defining parameters

Level: \( N \) = \( 5280 = 2^{5} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(2949120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5280))\).

Total New Old
Modular forms 747520 281448 466072
Cusp forms 727041 279288 447753
Eisenstein series 20479 2160 18319

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5280))\)

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
5280.2.a \(\chi_{5280}(1, \cdot)\) 5280.2.a.a 1 1
5280.2.a.b 1
5280.2.a.c 1
5280.2.a.d 1
5280.2.a.e 1
5280.2.a.f 1
5280.2.a.g 1
5280.2.a.h 1
5280.2.a.i 1
5280.2.a.j 1
5280.2.a.k 1
5280.2.a.l 1
5280.2.a.m 1
5280.2.a.n 1
5280.2.a.o 1
5280.2.a.p 1
5280.2.a.q 1
5280.2.a.r 1
5280.2.a.s 1
5280.2.a.t 1
5280.2.a.u 2
5280.2.a.v 2
5280.2.a.w 2
5280.2.a.x 2
5280.2.a.y 2
5280.2.a.z 2
5280.2.a.ba 2
5280.2.a.bb 2
5280.2.a.bc 2
5280.2.a.bd 2
5280.2.a.be 2
5280.2.a.bf 2
5280.2.a.bg 2
5280.2.a.bh 2
5280.2.a.bi 2
5280.2.a.bj 2
5280.2.a.bk 3
5280.2.a.bl 3
5280.2.a.bm 3
5280.2.a.bn 3
5280.2.a.bo 4
5280.2.a.bp 4
5280.2.a.bq 4
5280.2.a.br 4
5280.2.d \(\chi_{5280}(3169, \cdot)\) n/a 120 1
5280.2.e \(\chi_{5280}(1871, \cdot)\) n/a 160 1
5280.2.f \(\chi_{5280}(1121, \cdot)\) n/a 192 1
5280.2.g \(\chi_{5280}(4399, \cdot)\) n/a 144 1
5280.2.j \(\chi_{5280}(529, \cdot)\) n/a 120 1
5280.2.k \(\chi_{5280}(4511, \cdot)\) n/a 160 1
5280.2.p \(\chi_{5280}(3761, \cdot)\) n/a 192 1
5280.2.q \(\chi_{5280}(1759, \cdot)\) n/a 144 1
5280.2.t \(\chi_{5280}(3871, \cdot)\) 5280.2.t.a 4 1
5280.2.t.b 4
5280.2.t.c 4
5280.2.t.d 20
5280.2.t.e 20
5280.2.t.f 20
5280.2.t.g 24
5280.2.u \(\chi_{5280}(1649, \cdot)\) n/a 280 1
5280.2.v \(\chi_{5280}(2399, \cdot)\) n/a 240 1
5280.2.w \(\chi_{5280}(2641, \cdot)\) 5280.2.w.a 2 1
5280.2.w.b 2
5280.2.w.c 12
5280.2.w.d 18
5280.2.w.e 20
5280.2.w.f 26
5280.2.z \(\chi_{5280}(1231, \cdot)\) 5280.2.z.a 4 1
5280.2.z.b 4
5280.2.z.c 40
5280.2.z.d 48
5280.2.ba \(\chi_{5280}(4289, \cdot)\) n/a 288 1
5280.2.bf \(\chi_{5280}(5039, \cdot)\) n/a 240 1
5280.2.bh \(\chi_{5280}(329, \cdot)\) None 0 2
5280.2.bi \(\chi_{5280}(2551, \cdot)\) None 0 2
5280.2.bl \(\chi_{5280}(1321, \cdot)\) None 0 2
5280.2.bm \(\chi_{5280}(1079, \cdot)\) None 0 2
5280.2.bo \(\chi_{5280}(1783, \cdot)\) None 0 2
5280.2.bq \(\chi_{5280}(263, \cdot)\) None 0 2
5280.2.bt \(\chi_{5280}(1673, \cdot)\) None 0 2
5280.2.bv \(\chi_{5280}(3673, \cdot)\) None 0 2
5280.2.bx \(\chi_{5280}(3167, \cdot)\) n/a 576 2
5280.2.by \(\chi_{5280}(1297, \cdot)\) n/a 288 2
5280.2.cb \(\chi_{5280}(463, \cdot)\) n/a 240 2
5280.2.cc \(\chi_{5280}(353, \cdot)\) n/a 480 2
5280.2.cf \(\chi_{5280}(2047, \cdot)\) n/a 240 2
5280.2.cg \(\chi_{5280}(1937, \cdot)\) n/a 480 2
5280.2.cj \(\chi_{5280}(527, \cdot)\) n/a 560 2
5280.2.ck \(\chi_{5280}(3937, \cdot)\) n/a 288 2
5280.2.cm \(\chi_{5280}(2903, \cdot)\) None 0 2
5280.2.co \(\chi_{5280}(727, \cdot)\) None 0 2
5280.2.cr \(\chi_{5280}(1033, \cdot)\) None 0 2
5280.2.ct \(\chi_{5280}(617, \cdot)\) None 0 2
5280.2.cu \(\chi_{5280}(551, \cdot)\) None 0 2
5280.2.cx \(\chi_{5280}(1849, \cdot)\) None 0 2
5280.2.cy \(\chi_{5280}(439, \cdot)\) None 0 2
5280.2.db \(\chi_{5280}(2441, \cdot)\) None 0 2
5280.2.dc \(\chi_{5280}(961, \cdot)\) n/a 384 4
5280.2.dd \(\chi_{5280}(67, \cdot)\) n/a 1920 4
5280.2.de \(\chi_{5280}(2243, \cdot)\) n/a 4576 4
5280.2.dj \(\chi_{5280}(373, \cdot)\) n/a 2304 4
5280.2.dk \(\chi_{5280}(2333, \cdot)\) n/a 3840 4
5280.2.dl \(\chi_{5280}(1099, \cdot)\) n/a 2304 4
5280.2.dn \(\chi_{5280}(419, \cdot)\) n/a 3840 4
5280.2.dq \(\chi_{5280}(661, \cdot)\) n/a 1280 4
5280.2.ds \(\chi_{5280}(461, \cdot)\) n/a 3072 4
5280.2.du \(\chi_{5280}(1211, \cdot)\) n/a 2560 4
5280.2.dw \(\chi_{5280}(571, \cdot)\) n/a 1536 4
5280.2.dx \(\chi_{5280}(989, \cdot)\) n/a 4576 4
5280.2.dz \(\chi_{5280}(1189, \cdot)\) n/a 1920 4
5280.2.ed \(\chi_{5280}(1693, \cdot)\) n/a 2304 4
5280.2.ee \(\chi_{5280}(1013, \cdot)\) n/a 3840 4
5280.2.ef \(\chi_{5280}(1123, \cdot)\) n/a 1920 4
5280.2.eg \(\chi_{5280}(923, \cdot)\) n/a 4576 4
5280.2.ej \(\chi_{5280}(719, \cdot)\) n/a 1120 4
5280.2.eo \(\chi_{5280}(271, \cdot)\) n/a 384 4
5280.2.ep \(\chi_{5280}(1889, \cdot)\) n/a 1152 4
5280.2.es \(\chi_{5280}(1439, \cdot)\) n/a 1152 4
5280.2.et \(\chi_{5280}(1681, \cdot)\) n/a 384 4
5280.2.eu \(\chi_{5280}(1471, \cdot)\) n/a 384 4
5280.2.ev \(\chi_{5280}(689, \cdot)\) n/a 1120 4
5280.2.ey \(\chi_{5280}(1361, \cdot)\) n/a 768 4
5280.2.ez \(\chi_{5280}(799, \cdot)\) n/a 576 4
5280.2.fe \(\chi_{5280}(49, \cdot)\) n/a 576 4
5280.2.ff \(\chi_{5280}(191, \cdot)\) n/a 768 4
5280.2.fi \(\chi_{5280}(161, \cdot)\) n/a 768 4
5280.2.fj \(\chi_{5280}(79, \cdot)\) n/a 576 4
5280.2.fk \(\chi_{5280}(289, \cdot)\) n/a 576 4
5280.2.fl \(\chi_{5280}(911, \cdot)\) n/a 768 4
5280.2.fp \(\chi_{5280}(679, \cdot)\) None 0 8
5280.2.fq \(\chi_{5280}(41, \cdot)\) None 0 8
5280.2.ft \(\chi_{5280}(71, \cdot)\) None 0 8
5280.2.fu \(\chi_{5280}(169, \cdot)\) None 0 8
5280.2.fw \(\chi_{5280}(137, \cdot)\) None 0 8
5280.2.fy \(\chi_{5280}(73, \cdot)\) None 0 8
5280.2.gb \(\chi_{5280}(103, \cdot)\) None 0 8
5280.2.gd \(\chi_{5280}(167, \cdot)\) None 0 8
5280.2.gf \(\chi_{5280}(193, \cdot)\) n/a 1152 8
5280.2.gg \(\chi_{5280}(623, \cdot)\) n/a 2240 8
5280.2.gj \(\chi_{5280}(113, \cdot)\) n/a 2240 8
5280.2.gk \(\chi_{5280}(223, \cdot)\) n/a 1152 8
5280.2.gn \(\chi_{5280}(257, \cdot)\) n/a 2304 8
5280.2.go \(\chi_{5280}(367, \cdot)\) n/a 1152 8
5280.2.gr \(\chi_{5280}(337, \cdot)\) n/a 1152 8
5280.2.gs \(\chi_{5280}(767, \cdot)\) n/a 2304 8
5280.2.gu \(\chi_{5280}(457, \cdot)\) None 0 8
5280.2.gw \(\chi_{5280}(377, \cdot)\) None 0 8
5280.2.gz \(\chi_{5280}(743, \cdot)\) None 0 8
5280.2.hb \(\chi_{5280}(487, \cdot)\) None 0 8
5280.2.hc \(\chi_{5280}(361, \cdot)\) None 0 8
5280.2.hf \(\chi_{5280}(119, \cdot)\) None 0 8
5280.2.hg \(\chi_{5280}(569, \cdot)\) None 0 8
5280.2.hj \(\chi_{5280}(151, \cdot)\) None 0 8
5280.2.hk \(\chi_{5280}(53, \cdot)\) n/a 18304 16
5280.2.hl \(\chi_{5280}(13, \cdot)\) n/a 9216 16
5280.2.hq \(\chi_{5280}(227, \cdot)\) n/a 18304 16
5280.2.hr \(\chi_{5280}(163, \cdot)\) n/a 9216 16
5280.2.ht \(\chi_{5280}(229, \cdot)\) n/a 9216 16
5280.2.hv \(\chi_{5280}(29, \cdot)\) n/a 18304 16
5280.2.hw \(\chi_{5280}(211, \cdot)\) n/a 6144 16
5280.2.hy \(\chi_{5280}(251, \cdot)\) n/a 12288 16
5280.2.ia \(\chi_{5280}(101, \cdot)\) n/a 12288 16
5280.2.ic \(\chi_{5280}(181, \cdot)\) n/a 6144 16
5280.2.if \(\chi_{5280}(59, \cdot)\) n/a 18304 16
5280.2.ih \(\chi_{5280}(19, \cdot)\) n/a 9216 16
5280.2.ik \(\chi_{5280}(83, \cdot)\) n/a 18304 16
5280.2.il \(\chi_{5280}(763, \cdot)\) n/a 9216 16
5280.2.im \(\chi_{5280}(653, \cdot)\) n/a 18304 16
5280.2.in \(\chi_{5280}(613, \cdot)\) n/a 9216 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1056))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5280))\)\(^{\oplus 1}\)