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Properties

Label 4032.3
Level 4032
Weight 3
Dimension 376578
Nonzero newspaces 80
Sturm bound 2654208

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(2654208\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(4032))\).

Total New Old
Modular forms 891648 378558 513090
Cusp forms 877824 376578 501246
Eisenstein series 13824 1980 11844

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(4032))\)

We only show spaces with odd 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
4032.3.d \(\chi_{4032}(449, \cdot)\) 4032.3.d.a 4 1
4032.3.d.b 4
4032.3.d.c 4
4032.3.d.d 4
4032.3.d.e 4
4032.3.d.f 4
4032.3.d.g 4
4032.3.d.h 4
4032.3.d.i 4
4032.3.d.j 4
4032.3.d.k 4
4032.3.d.l 8
4032.3.d.m 8
4032.3.d.n 12
4032.3.d.o 12
4032.3.d.p 12
4032.3.e \(\chi_{4032}(2015, \cdot)\) n/a 128 1
4032.3.f \(\chi_{4032}(3457, \cdot)\) n/a 158 1
4032.3.g \(\chi_{4032}(2143, \cdot)\) n/a 120 1
4032.3.l \(\chi_{4032}(1441, \cdot)\) n/a 160 1
4032.3.m \(\chi_{4032}(127, \cdot)\) n/a 120 1
4032.3.n \(\chi_{4032}(2465, \cdot)\) 4032.3.n.a 16 1
4032.3.n.b 16
4032.3.n.c 64
4032.3.o \(\chi_{4032}(4031, \cdot)\) n/a 128 1
4032.3.u \(\chi_{4032}(433, \cdot)\) n/a 316 2
4032.3.w \(\chi_{4032}(1457, \cdot)\) n/a 192 2
4032.3.y \(\chi_{4032}(1007, \cdot)\) n/a 256 2
4032.3.ba \(\chi_{4032}(1135, \cdot)\) n/a 240 2
4032.3.bc \(\chi_{4032}(1055, \cdot)\) n/a 768 2
4032.3.bd \(\chi_{4032}(65, \cdot)\) n/a 760 2
4032.3.bi \(\chi_{4032}(2335, \cdot)\) n/a 768 2
4032.3.bj \(\chi_{4032}(1921, \cdot)\) n/a 760 2
4032.3.bk \(\chi_{4032}(1151, \cdot)\) n/a 256 2
4032.3.bl \(\chi_{4032}(737, \cdot)\) n/a 256 2
4032.3.bo \(\chi_{4032}(1121, \cdot)\) n/a 576 2
4032.3.bp \(\chi_{4032}(383, \cdot)\) n/a 760 2
4032.3.bq \(\chi_{4032}(2657, \cdot)\) n/a 768 2
4032.3.br \(\chi_{4032}(1343, \cdot)\) n/a 760 2
4032.3.bv \(\chi_{4032}(97, \cdot)\) n/a 768 2
4032.3.bw \(\chi_{4032}(1663, \cdot)\) n/a 760 2
4032.3.bx \(\chi_{4032}(481, \cdot)\) n/a 768 2
4032.3.by \(\chi_{4032}(1471, \cdot)\) n/a 576 2
4032.3.cd \(\chi_{4032}(2431, \cdot)\) n/a 316 2
4032.3.ce \(\chi_{4032}(2593, \cdot)\) n/a 320 2
4032.3.cf \(\chi_{4032}(415, \cdot)\) n/a 320 2
4032.3.cg \(\chi_{4032}(577, \cdot)\) n/a 316 2
4032.3.cl \(\chi_{4032}(769, \cdot)\) n/a 760 2
4032.3.cm \(\chi_{4032}(1759, \cdot)\) n/a 768 2
4032.3.cn \(\chi_{4032}(2497, \cdot)\) n/a 760 2
4032.3.co \(\chi_{4032}(799, \cdot)\) n/a 576 2
4032.3.ct \(\chi_{4032}(1793, \cdot)\) n/a 576 2
4032.3.cu \(\chi_{4032}(479, \cdot)\) n/a 768 2
4032.3.cv \(\chi_{4032}(641, \cdot)\) n/a 760 2
4032.3.cw \(\chi_{4032}(671, \cdot)\) n/a 768 2
4032.3.db \(\chi_{4032}(3167, \cdot)\) n/a 256 2
4032.3.dc \(\chi_{4032}(2753, \cdot)\) n/a 256 2
4032.3.dd \(\chi_{4032}(319, \cdot)\) n/a 760 2
4032.3.de \(\chi_{4032}(1825, \cdot)\) n/a 768 2
4032.3.di \(\chi_{4032}(3071, \cdot)\) n/a 760 2
4032.3.dj \(\chi_{4032}(2081, \cdot)\) n/a 768 2
4032.3.dl \(\chi_{4032}(631, \cdot)\) None 0 4
4032.3.dn \(\chi_{4032}(503, \cdot)\) None 0 4
4032.3.dp \(\chi_{4032}(937, \cdot)\) None 0 4
4032.3.dr \(\chi_{4032}(953, \cdot)\) None 0 4
4032.3.dt \(\chi_{4032}(113, \cdot)\) n/a 1152 4
4032.3.dv \(\chi_{4032}(1105, \cdot)\) n/a 1520 4
4032.3.dx \(\chi_{4032}(47, \cdot)\) n/a 1520 4
4032.3.dy \(\chi_{4032}(655, \cdot)\) n/a 1520 4
4032.3.eb \(\chi_{4032}(1423, \cdot)\) n/a 632 4
4032.3.ed \(\chi_{4032}(143, \cdot)\) n/a 512 4
4032.3.ee \(\chi_{4032}(1391, \cdot)\) n/a 1520 4
4032.3.eh \(\chi_{4032}(79, \cdot)\) n/a 1520 4
4032.3.ej \(\chi_{4032}(817, \cdot)\) n/a 1520 4
4032.3.el \(\chi_{4032}(305, \cdot)\) n/a 512 4
4032.3.em \(\chi_{4032}(401, \cdot)\) n/a 1520 4
4032.3.eo \(\chi_{4032}(241, \cdot)\) n/a 1520 4
4032.3.er \(\chi_{4032}(145, \cdot)\) n/a 632 4
4032.3.et \(\chi_{4032}(977, \cdot)\) n/a 1520 4
4032.3.ev \(\chi_{4032}(463, \cdot)\) n/a 1152 4
4032.3.ex \(\chi_{4032}(335, \cdot)\) n/a 1520 4
4032.3.ey \(\chi_{4032}(251, \cdot)\) n/a 4096 8
4032.3.ez \(\chi_{4032}(197, \cdot)\) n/a 3072 8
4032.3.fe \(\chi_{4032}(181, \cdot)\) n/a 5104 8
4032.3.ff \(\chi_{4032}(379, \cdot)\) n/a 3840 8
4032.3.fg \(\chi_{4032}(167, \cdot)\) None 0 8
4032.3.fi \(\chi_{4032}(295, \cdot)\) None 0 8
4032.3.fl \(\chi_{4032}(745, \cdot)\) None 0 8
4032.3.fm \(\chi_{4032}(473, \cdot)\) None 0 8
4032.3.fn \(\chi_{4032}(233, \cdot)\) None 0 8
4032.3.fq \(\chi_{4032}(73, \cdot)\) None 0 8
4032.3.fr \(\chi_{4032}(313, \cdot)\) None 0 8
4032.3.fv \(\chi_{4032}(137, \cdot)\) None 0 8
4032.3.fx \(\chi_{4032}(151, \cdot)\) None 0 8
4032.3.fy \(\chi_{4032}(215, \cdot)\) None 0 8
4032.3.fz \(\chi_{4032}(311, \cdot)\) None 0 8
4032.3.gc \(\chi_{4032}(583, \cdot)\) None 0 8
4032.3.gd \(\chi_{4032}(487, \cdot)\) None 0 8
4032.3.gh \(\chi_{4032}(887, \cdot)\) None 0 8
4032.3.gi \(\chi_{4032}(281, \cdot)\) None 0 8
4032.3.gk \(\chi_{4032}(265, \cdot)\) None 0 8
4032.3.gm \(\chi_{4032}(131, \cdot)\) n/a 24512 16
4032.3.gn \(\chi_{4032}(149, \cdot)\) n/a 24512 16
4032.3.gq \(\chi_{4032}(163, \cdot)\) n/a 10208 16
4032.3.gr \(\chi_{4032}(43, \cdot)\) n/a 18432 16
4032.3.gs \(\chi_{4032}(67, \cdot)\) n/a 24512 16
4032.3.gt \(\chi_{4032}(61, \cdot)\) n/a 24512 16
4032.3.gu \(\chi_{4032}(13, \cdot)\) n/a 24512 16
4032.3.gv \(\chi_{4032}(325, \cdot)\) n/a 10208 16
4032.3.hi \(\chi_{4032}(53, \cdot)\) n/a 8192 16
4032.3.hj \(\chi_{4032}(221, \cdot)\) n/a 24512 16
4032.3.hk \(\chi_{4032}(29, \cdot)\) n/a 18432 16
4032.3.hl \(\chi_{4032}(83, \cdot)\) n/a 24512 16
4032.3.hm \(\chi_{4032}(59, \cdot)\) n/a 24512 16
4032.3.hn \(\chi_{4032}(395, \cdot)\) n/a 8192 16
4032.3.hq \(\chi_{4032}(229, \cdot)\) n/a 24512 16
4032.3.hr \(\chi_{4032}(403, \cdot)\) n/a 24512 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(4032))\) into lower level spaces

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