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Properties

Label 8064.2
Level 8064
Weight 2
Dimension 752976
Nonzero newspaces 100
Sturm bound 7077888

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Defining parameters

Level: \( N \) = \( 8064 = 2^{7} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(7077888\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8064))\).

Total New Old
Modular forms 1784832 757296 1027536
Cusp forms 1754113 752976 1001137
Eisenstein series 30719 4320 26399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8064))\)

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
8064.2.a \(\chi_{8064}(1, \cdot)\) 8064.2.a.a 1 1
8064.2.a.b 1
8064.2.a.c 1
8064.2.a.d 1
8064.2.a.e 1
8064.2.a.f 1
8064.2.a.g 1
8064.2.a.h 1
8064.2.a.i 1
8064.2.a.j 1
8064.2.a.k 1
8064.2.a.l 1
8064.2.a.m 1
8064.2.a.n 1
8064.2.a.o 1
8064.2.a.p 1
8064.2.a.q 1
8064.2.a.r 1
8064.2.a.s 1
8064.2.a.t 1
8064.2.a.u 1
8064.2.a.v 1
8064.2.a.w 1
8064.2.a.x 1
8064.2.a.y 1
8064.2.a.z 1
8064.2.a.ba 1
8064.2.a.bb 1
8064.2.a.bc 2
8064.2.a.bd 2
8064.2.a.be 2
8064.2.a.bf 2
8064.2.a.bg 2
8064.2.a.bh 2
8064.2.a.bi 2
8064.2.a.bj 2
8064.2.a.bk 2
8064.2.a.bl 2
8064.2.a.bm 2
8064.2.a.bn 2
8064.2.a.bo 2
8064.2.a.bp 2
8064.2.a.bq 2
8064.2.a.br 2
8064.2.a.bs 3
8064.2.a.bt 3
8064.2.a.bu 3
8064.2.a.bv 3
8064.2.a.bw 3
8064.2.a.bx 3
8064.2.a.by 3
8064.2.a.bz 3
8064.2.a.ca 3
8064.2.a.cb 3
8064.2.a.cc 3
8064.2.a.cd 3
8064.2.a.ce 3
8064.2.a.cf 3
8064.2.a.cg 3
8064.2.a.ch 3
8064.2.a.ci 3
8064.2.a.cj 3
8064.2.a.ck 3
8064.2.a.cl 3
8064.2.b \(\chi_{8064}(3583, \cdot)\) n/a 160 1
8064.2.c \(\chi_{8064}(4033, \cdot)\) n/a 120 1
8064.2.h \(\chi_{8064}(4607, \cdot)\) 8064.2.h.a 12 1
8064.2.h.b 12
8064.2.h.c 12
8064.2.h.d 12
8064.2.h.e 12
8064.2.h.f 12
8064.2.h.g 12
8064.2.h.h 12
8064.2.i \(\chi_{8064}(3905, \cdot)\) n/a 128 1
8064.2.j \(\chi_{8064}(575, \cdot)\) 8064.2.j.a 4 1
8064.2.j.b 4
8064.2.j.c 12
8064.2.j.d 12
8064.2.j.e 12
8064.2.j.f 12
8064.2.j.g 12
8064.2.j.h 12
8064.2.j.i 16
8064.2.k \(\chi_{8064}(7937, \cdot)\) n/a 128 1
8064.2.p \(\chi_{8064}(7615, \cdot)\) n/a 160 1
8064.2.q \(\chi_{8064}(1537, \cdot)\) n/a 768 2
8064.2.r \(\chi_{8064}(2689, \cdot)\) n/a 576 2
8064.2.s \(\chi_{8064}(2305, \cdot)\) n/a 320 2
8064.2.t \(\chi_{8064}(4225, \cdot)\) n/a 768 2
8064.2.v \(\chi_{8064}(2591, \cdot)\) n/a 192 2
8064.2.x \(\chi_{8064}(1567, \cdot)\) n/a 312 2
8064.2.z \(\chi_{8064}(2017, \cdot)\) n/a 240 2
8064.2.bb \(\chi_{8064}(1889, \cdot)\) n/a 256 2
8064.2.be \(\chi_{8064}(193, \cdot)\) n/a 768 2
8064.2.bf \(\chi_{8064}(2047, \cdot)\) n/a 768 2
8064.2.bg \(\chi_{8064}(6977, \cdot)\) n/a 768 2
8064.2.bh \(\chi_{8064}(4223, \cdot)\) n/a 768 2
8064.2.bm \(\chi_{8064}(2239, \cdot)\) n/a 768 2
8064.2.bn \(\chi_{8064}(2623, \cdot)\) n/a 768 2
8064.2.bs \(\chi_{8064}(703, \cdot)\) n/a 320 2
8064.2.bt \(\chi_{8064}(1025, \cdot)\) n/a 256 2
8064.2.bu \(\chi_{8064}(2879, \cdot)\) n/a 256 2
8064.2.bz \(\chi_{8064}(3263, \cdot)\) n/a 576 2
8064.2.ca \(\chi_{8064}(257, \cdot)\) n/a 768 2
8064.2.cb \(\chi_{8064}(4799, \cdot)\) n/a 768 2
8064.2.cc \(\chi_{8064}(2561, \cdot)\) n/a 768 2
8064.2.ch \(\chi_{8064}(1919, \cdot)\) n/a 576 2
8064.2.ci \(\chi_{8064}(2369, \cdot)\) n/a 768 2
8064.2.cj \(\chi_{8064}(767, \cdot)\) n/a 768 2
8064.2.ck \(\chi_{8064}(1217, \cdot)\) n/a 768 2
8064.2.cp \(\chi_{8064}(1601, \cdot)\) n/a 256 2
8064.2.cq \(\chi_{8064}(3455, \cdot)\) n/a 256 2
8064.2.cr \(\chi_{8064}(2881, \cdot)\) n/a 320 2
8064.2.cs \(\chi_{8064}(1279, \cdot)\) n/a 320 2
8064.2.cx \(\chi_{8064}(895, \cdot)\) n/a 768 2
8064.2.cy \(\chi_{8064}(3649, \cdot)\) n/a 768 2
8064.2.cz \(\chi_{8064}(6655, \cdot)\) n/a 768 2
8064.2.da \(\chi_{8064}(1345, \cdot)\) n/a 576 2
8064.2.df \(\chi_{8064}(2945, \cdot)\) n/a 768 2
8064.2.dg \(\chi_{8064}(191, \cdot)\) n/a 768 2
8064.2.dh \(\chi_{8064}(6079, \cdot)\) n/a 768 2
8064.2.dk \(\chi_{8064}(881, \cdot)\) n/a 512 4
8064.2.dm \(\chi_{8064}(1009, \cdot)\) n/a 480 4
8064.2.do \(\chi_{8064}(1583, \cdot)\) n/a 384 4
8064.2.dq \(\chi_{8064}(559, \cdot)\) n/a 632 4
8064.2.ds \(\chi_{8064}(223, \cdot)\) n/a 1504 4
8064.2.du \(\chi_{8064}(1247, \cdot)\) n/a 1152 4
8064.2.dw \(\chi_{8064}(2209, \cdot)\) n/a 1504 4
8064.2.dz \(\chi_{8064}(353, \cdot)\) n/a 1504 4
8064.2.ea \(\chi_{8064}(3041, \cdot)\) n/a 512 4
8064.2.ec \(\chi_{8064}(289, \cdot)\) n/a 624 4
8064.2.ef \(\chi_{8064}(1633, \cdot)\) n/a 1504 4
8064.2.eg \(\chi_{8064}(929, \cdot)\) n/a 1504 4
8064.2.ei \(\chi_{8064}(95, \cdot)\) n/a 1504 4
8064.2.ek \(\chi_{8064}(2719, \cdot)\) n/a 624 4
8064.2.en \(\chi_{8064}(607, \cdot)\) n/a 1504 4
8064.2.ep \(\chi_{8064}(2783, \cdot)\) n/a 1504 4
8064.2.eq \(\chi_{8064}(863, \cdot)\) n/a 512 4
8064.2.es \(\chi_{8064}(31, \cdot)\) n/a 1504 4
8064.2.eu \(\chi_{8064}(545, \cdot)\) n/a 1504 4
8064.2.ew \(\chi_{8064}(673, \cdot)\) n/a 1152 4
8064.2.fa \(\chi_{8064}(505, \cdot)\) None 0 8
8064.2.fb \(\chi_{8064}(55, \cdot)\) None 0 8
8064.2.fc \(\chi_{8064}(71, \cdot)\) None 0 8
8064.2.fd \(\chi_{8064}(377, \cdot)\) None 0 8
8064.2.fh \(\chi_{8064}(337, \cdot)\) n/a 2304 8
8064.2.fj \(\chi_{8064}(209, \cdot)\) n/a 3040 8
8064.2.fk \(\chi_{8064}(527, \cdot)\) n/a 3040 8
8064.2.fo \(\chi_{8064}(271, \cdot)\) n/a 1264 8
8064.2.fp \(\chi_{8064}(943, \cdot)\) n/a 3040 8
8064.2.fs \(\chi_{8064}(1103, \cdot)\) n/a 3040 8
8064.2.ft \(\chi_{8064}(431, \cdot)\) n/a 1024 8
8064.2.fu \(\chi_{8064}(367, \cdot)\) n/a 3040 8
8064.2.fw \(\chi_{8064}(1265, \cdot)\) n/a 3040 8
8064.2.ga \(\chi_{8064}(1201, \cdot)\) n/a 3040 8
8064.2.gb \(\chi_{8064}(1297, \cdot)\) n/a 1264 8
8064.2.ge \(\chi_{8064}(17, \cdot)\) n/a 1024 8
8064.2.gf \(\chi_{8064}(689, \cdot)\) n/a 3040 8
8064.2.gg \(\chi_{8064}(529, \cdot)\) n/a 3040 8
8064.2.gj \(\chi_{8064}(1231, \cdot)\) n/a 3040 8
8064.2.gl \(\chi_{8064}(239, \cdot)\) n/a 2304 8
8064.2.gm \(\chi_{8064}(307, \cdot)\) n/a 10208 16
8064.2.gp \(\chi_{8064}(253, \cdot)\) n/a 7680 16
8064.2.gq \(\chi_{8064}(323, \cdot)\) n/a 6144 16
8064.2.gt \(\chi_{8064}(125, \cdot)\) n/a 8192 16
8064.2.gw \(\chi_{8064}(25, \cdot)\) None 0 16
8064.2.gx \(\chi_{8064}(103, \cdot)\) None 0 16
8064.2.he \(\chi_{8064}(41, \cdot)\) None 0 16
8064.2.hf \(\chi_{8064}(185, \cdot)\) None 0 16
8064.2.hg \(\chi_{8064}(89, \cdot)\) None 0 16
8064.2.hh \(\chi_{8064}(359, \cdot)\) None 0 16
8064.2.hi \(\chi_{8064}(599, \cdot)\) None 0 16
8064.2.hj \(\chi_{8064}(407, \cdot)\) None 0 16
8064.2.hk \(\chi_{8064}(439, \cdot)\) None 0 16
8064.2.hl \(\chi_{8064}(391, \cdot)\) None 0 16
8064.2.hm \(\chi_{8064}(199, \cdot)\) None 0 16
8064.2.hn \(\chi_{8064}(361, \cdot)\) None 0 16
8064.2.ho \(\chi_{8064}(169, \cdot)\) None 0 16
8064.2.hp \(\chi_{8064}(457, \cdot)\) None 0 16
8064.2.hw \(\chi_{8064}(23, \cdot)\) None 0 16
8064.2.hx \(\chi_{8064}(761, \cdot)\) None 0 16
8064.2.ib \(\chi_{8064}(115, \cdot)\) n/a 49024 32
8064.2.ic \(\chi_{8064}(277, \cdot)\) n/a 49024 32
8064.2.ie \(\chi_{8064}(347, \cdot)\) n/a 49024 32
8064.2.ih \(\chi_{8064}(155, \cdot)\) n/a 36864 32
8064.2.ii \(\chi_{8064}(107, \cdot)\) n/a 16384 32
8064.2.il \(\chi_{8064}(269, \cdot)\) n/a 16384 32
8064.2.im \(\chi_{8064}(293, \cdot)\) n/a 49024 32
8064.2.ip \(\chi_{8064}(173, \cdot)\) n/a 49024 32
8064.2.iq \(\chi_{8064}(187, \cdot)\) n/a 49024 32
8064.2.it \(\chi_{8064}(19, \cdot)\) n/a 20416 32
8064.2.iu \(\chi_{8064}(139, \cdot)\) n/a 49024 32
8064.2.ix \(\chi_{8064}(85, \cdot)\) n/a 36864 32
8064.2.iy \(\chi_{8064}(37, \cdot)\) n/a 20416 32
8064.2.jb \(\chi_{8064}(205, \cdot)\) n/a 49024 32
8064.2.jd \(\chi_{8064}(11, \cdot)\) n/a 49024 32
8064.2.je \(\chi_{8064}(5, \cdot)\) n/a 49024 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8064)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 42}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2016))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2688))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4032))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8064))\)\(^{\oplus 1}\)