# Properties

 Label 4032.2 Level 4032 Weight 2 Dimension 187794 Nonzero newspaces 80 Sturm bound 1.76947e+06

## 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 the 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

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