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Properties

Label 4032.2
Level 4032
Weight 2
Dimension 187794
Nonzero newspaces 80
Sturm bound 1769472

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(1769472\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4032))\).

Total New Old
Modular forms 449280 189774 259506
Cusp forms 435457 187794 247663
Eisenstein series 13823 1980 11843

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4032))\)

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
4032.2.a \(\chi_{4032}(1, \cdot)\) 4032.2.a.a 1 1
4032.2.a.b 1
4032.2.a.c 1
4032.2.a.d 1
4032.2.a.e 1
4032.2.a.f 1
4032.2.a.g 1
4032.2.a.h 1
4032.2.a.i 1
4032.2.a.j 1
4032.2.a.k 1
4032.2.a.l 1
4032.2.a.m 1
4032.2.a.n 1
4032.2.a.o 1
4032.2.a.p 1
4032.2.a.q 1
4032.2.a.r 1
4032.2.a.s 1
4032.2.a.t 1
4032.2.a.u 1
4032.2.a.v 1
4032.2.a.w 1
4032.2.a.x 1
4032.2.a.y 1
4032.2.a.z 1
4032.2.a.ba 1
4032.2.a.bb 1
4032.2.a.bc 1
4032.2.a.bd 1
4032.2.a.be 1
4032.2.a.bf 1
4032.2.a.bg 1
4032.2.a.bh 1
4032.2.a.bi 1
4032.2.a.bj 1
4032.2.a.bk 1
4032.2.a.bl 1
4032.2.a.bm 1
4032.2.a.bn 1
4032.2.a.bo 2
4032.2.a.bp 2
4032.2.a.bq 2
4032.2.a.br 2
4032.2.a.bs 2
4032.2.a.bt 2
4032.2.a.bu 2
4032.2.a.bv 2
4032.2.a.bw 2
4032.2.a.bx 2
4032.2.b \(\chi_{4032}(3583, \cdot)\) 4032.2.b.a 2 1
4032.2.b.b 2
4032.2.b.c 2
4032.2.b.d 2
4032.2.b.e 2
4032.2.b.f 2
4032.2.b.g 2
4032.2.b.h 2
4032.2.b.i 2
4032.2.b.j 4
4032.2.b.k 4
4032.2.b.l 4
4032.2.b.m 4
4032.2.b.n 4
4032.2.b.o 8
4032.2.b.p 8
4032.2.b.q 8
4032.2.b.r 16
4032.2.c \(\chi_{4032}(2017, \cdot)\) 4032.2.c.a 2 1
4032.2.c.b 2
4032.2.c.c 2
4032.2.c.d 2
4032.2.c.e 2
4032.2.c.f 2
4032.2.c.g 2
4032.2.c.h 2
4032.2.c.i 2
4032.2.c.j 2
4032.2.c.k 4
4032.2.c.l 4
4032.2.c.m 4
4032.2.c.n 4
4032.2.c.o 4
4032.2.c.p 4
4032.2.c.q 8
4032.2.c.r 8
4032.2.h \(\chi_{4032}(575, \cdot)\) 4032.2.h.a 4 1
4032.2.h.b 4
4032.2.h.c 4
4032.2.h.d 4
4032.2.h.e 4
4032.2.h.f 8
4032.2.h.g 8
4032.2.h.h 12
4032.2.i \(\chi_{4032}(1889, \cdot)\) 4032.2.i.a 8 1
4032.2.i.b 8
4032.2.i.c 48
4032.2.j \(\chi_{4032}(2591, \cdot)\) 4032.2.j.a 4 1
4032.2.j.b 4
4032.2.j.c 4
4032.2.j.d 4
4032.2.j.e 16
4032.2.j.f 16
4032.2.k \(\chi_{4032}(3905, \cdot)\) 4032.2.k.a 4 1
4032.2.k.b 4
4032.2.k.c 4
4032.2.k.d 4
4032.2.k.e 8
4032.2.k.f 8
4032.2.k.g 16
4032.2.k.h 16
4032.2.p \(\chi_{4032}(1567, \cdot)\) 4032.2.p.a 4 1
4032.2.p.b 4
4032.2.p.c 4
4032.2.p.d 4
4032.2.p.e 8
4032.2.p.f 8
4032.2.p.g 8
4032.2.p.h 8
4032.2.p.i 8
4032.2.p.j 12
4032.2.p.k 12
4032.2.q \(\chi_{4032}(1537, \cdot)\) n/a 376 2
4032.2.r \(\chi_{4032}(1345, \cdot)\) n/a 288 2
4032.2.s \(\chi_{4032}(2305, \cdot)\) n/a 156 2
4032.2.t \(\chi_{4032}(193, \cdot)\) n/a 376 2
4032.2.v \(\chi_{4032}(1583, \cdot)\) 4032.2.v.a 4 2
4032.2.v.b 4
4032.2.v.c 12
4032.2.v.d 36
4032.2.v.e 40
4032.2.x \(\chi_{4032}(559, \cdot)\) n/a 156 2
4032.2.z \(\chi_{4032}(1009, \cdot)\) n/a 120 2
4032.2.bb \(\chi_{4032}(881, \cdot)\) n/a 128 2
4032.2.be \(\chi_{4032}(2209, \cdot)\) n/a 384 2
4032.2.bf \(\chi_{4032}(2047, \cdot)\) n/a 376 2
4032.2.bg \(\chi_{4032}(929, \cdot)\) n/a 384 2
4032.2.bh \(\chi_{4032}(191, \cdot)\) n/a 376 2
4032.2.bm \(\chi_{4032}(223, \cdot)\) n/a 384 2
4032.2.bn \(\chi_{4032}(607, \cdot)\) n/a 384 2
4032.2.bs \(\chi_{4032}(2719, \cdot)\) n/a 160 2
4032.2.bt \(\chi_{4032}(1025, \cdot)\) n/a 128 2
4032.2.bu \(\chi_{4032}(863, \cdot)\) n/a 128 2
4032.2.bz \(\chi_{4032}(1247, \cdot)\) n/a 288 2
4032.2.ca \(\chi_{4032}(257, \cdot)\) n/a 376 2
4032.2.cb \(\chi_{4032}(2783, \cdot)\) n/a 384 2
4032.2.cc \(\chi_{4032}(1217, \cdot)\) n/a 376 2
4032.2.ch \(\chi_{4032}(1919, \cdot)\) n/a 288 2
4032.2.ci \(\chi_{4032}(353, \cdot)\) n/a 384 2
4032.2.cj \(\chi_{4032}(767, \cdot)\) n/a 376 2
4032.2.ck \(\chi_{4032}(545, \cdot)\) n/a 384 2
4032.2.cp \(\chi_{4032}(3041, \cdot)\) n/a 128 2
4032.2.cq \(\chi_{4032}(2879, \cdot)\) n/a 128 2
4032.2.cr \(\chi_{4032}(289, \cdot)\) n/a 160 2
4032.2.cs \(\chi_{4032}(703, \cdot)\) n/a 156 2
4032.2.cx \(\chi_{4032}(895, \cdot)\) n/a 376 2
4032.2.cy \(\chi_{4032}(1633, \cdot)\) n/a 384 2
4032.2.cz \(\chi_{4032}(2623, \cdot)\) n/a 376 2
4032.2.da \(\chi_{4032}(673, \cdot)\) n/a 288 2
4032.2.df \(\chi_{4032}(2945, \cdot)\) n/a 376 2
4032.2.dg \(\chi_{4032}(95, \cdot)\) n/a 384 2
4032.2.dh \(\chi_{4032}(31, \cdot)\) n/a 384 2
4032.2.dk \(\chi_{4032}(377, \cdot)\) None 0 4
4032.2.dm \(\chi_{4032}(505, \cdot)\) None 0 4
4032.2.do \(\chi_{4032}(71, \cdot)\) None 0 4
4032.2.dq \(\chi_{4032}(55, \cdot)\) None 0 4
4032.2.ds \(\chi_{4032}(1231, \cdot)\) n/a 752 4
4032.2.du \(\chi_{4032}(239, \cdot)\) n/a 576 4
4032.2.dw \(\chi_{4032}(1201, \cdot)\) n/a 752 4
4032.2.dz \(\chi_{4032}(1265, \cdot)\) n/a 752 4
4032.2.ea \(\chi_{4032}(17, \cdot)\) n/a 256 4
4032.2.ec \(\chi_{4032}(1297, \cdot)\) n/a 312 4
4032.2.ef \(\chi_{4032}(529, \cdot)\) n/a 752 4
4032.2.eg \(\chi_{4032}(689, \cdot)\) n/a 752 4
4032.2.ei \(\chi_{4032}(1103, \cdot)\) n/a 752 4
4032.2.ek \(\chi_{4032}(271, \cdot)\) n/a 312 4
4032.2.en \(\chi_{4032}(367, \cdot)\) n/a 752 4
4032.2.ep \(\chi_{4032}(527, \cdot)\) n/a 752 4
4032.2.eq \(\chi_{4032}(431, \cdot)\) n/a 256 4
4032.2.es \(\chi_{4032}(943, \cdot)\) n/a 752 4
4032.2.eu \(\chi_{4032}(209, \cdot)\) n/a 752 4
4032.2.ew \(\chi_{4032}(337, \cdot)\) n/a 576 4
4032.2.fa \(\chi_{4032}(253, \cdot)\) n/a 1920 8
4032.2.fb \(\chi_{4032}(307, \cdot)\) n/a 2544 8
4032.2.fc \(\chi_{4032}(323, \cdot)\) n/a 1536 8
4032.2.fd \(\chi_{4032}(125, \cdot)\) n/a 2048 8
4032.2.fh \(\chi_{4032}(169, \cdot)\) None 0 8
4032.2.fj \(\chi_{4032}(41, \cdot)\) None 0 8
4032.2.fk \(\chi_{4032}(23, \cdot)\) None 0 8
4032.2.fo \(\chi_{4032}(199, \cdot)\) None 0 8
4032.2.fp \(\chi_{4032}(439, \cdot)\) None 0 8
4032.2.fs \(\chi_{4032}(599, \cdot)\) None 0 8
4032.2.ft \(\chi_{4032}(359, \cdot)\) None 0 8
4032.2.fu \(\chi_{4032}(103, \cdot)\) None 0 8
4032.2.fw \(\chi_{4032}(761, \cdot)\) None 0 8
4032.2.ga \(\chi_{4032}(457, \cdot)\) None 0 8
4032.2.gb \(\chi_{4032}(361, \cdot)\) None 0 8
4032.2.ge \(\chi_{4032}(89, \cdot)\) None 0 8
4032.2.gf \(\chi_{4032}(185, \cdot)\) None 0 8
4032.2.gg \(\chi_{4032}(25, \cdot)\) None 0 8
4032.2.gj \(\chi_{4032}(391, \cdot)\) None 0 8
4032.2.gl \(\chi_{4032}(407, \cdot)\) None 0 8
4032.2.go \(\chi_{4032}(277, \cdot)\) n/a 12224 16
4032.2.gp \(\chi_{4032}(115, \cdot)\) n/a 12224 16
4032.2.gw \(\chi_{4032}(293, \cdot)\) n/a 12224 16
4032.2.gx \(\chi_{4032}(173, \cdot)\) n/a 12224 16
4032.2.gy \(\chi_{4032}(269, \cdot)\) n/a 4096 16
4032.2.gz \(\chi_{4032}(107, \cdot)\) n/a 4096 16
4032.2.ha \(\chi_{4032}(347, \cdot)\) n/a 12224 16
4032.2.hb \(\chi_{4032}(155, \cdot)\) n/a 9216 16
4032.2.hc \(\chi_{4032}(187, \cdot)\) n/a 12224 16
4032.2.hd \(\chi_{4032}(139, \cdot)\) n/a 12224 16
4032.2.he \(\chi_{4032}(19, \cdot)\) n/a 5088 16
4032.2.hf \(\chi_{4032}(37, \cdot)\) n/a 5088 16
4032.2.hg \(\chi_{4032}(85, \cdot)\) n/a 9216 16
4032.2.hh \(\chi_{4032}(205, \cdot)\) n/a 12224 16
4032.2.ho \(\chi_{4032}(11, \cdot)\) n/a 12224 16
4032.2.hp \(\chi_{4032}(5, \cdot)\) n/a 12224 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4032))\) into lower level spaces

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