Properties

Label 3024.1
Level 3024
Weight 1
Dimension 64
Nonzero newspaces 9
Newform subspaces 23
Sturm bound 497664
Trace bound 37

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Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 23 \)
Sturm bound: \(497664\)
Trace bound: \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3024))\).

Total New Old
Modular forms 5726 784 4942
Cusp forms 686 64 622
Eisenstein series 5040 720 4320

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 36 8 20 0

Trace form

\( 64q + 2q^{5} + 3q^{7} + O(q^{10}) \) \( 64q + 2q^{5} + 3q^{7} - 4q^{10} - 6q^{13} + 8q^{16} + 4q^{17} + 8q^{25} + 12q^{28} - 4q^{29} + 18q^{31} + 12q^{37} + 4q^{41} + 14q^{43} - 8q^{46} + q^{49} - 4q^{52} - 4q^{53} + 4q^{58} - 2q^{65} - 4q^{67} - 2q^{73} - 16q^{76} + 4q^{77} - 6q^{79} + 6q^{85} - 4q^{88} + 4q^{89} + 11q^{91} + 4q^{94} + 20q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3024))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3024.1.d \(\chi_{3024}(1457, \cdot)\) None 0 1
3024.1.e \(\chi_{3024}(1511, \cdot)\) None 0 1
3024.1.f \(\chi_{3024}(433, \cdot)\) 3024.1.f.a 2 1
3024.1.f.b 2
3024.1.g \(\chi_{3024}(2647, \cdot)\) None 0 1
3024.1.l \(\chi_{3024}(1945, \cdot)\) None 0 1
3024.1.m \(\chi_{3024}(1135, \cdot)\) None 0 1
3024.1.n \(\chi_{3024}(2969, \cdot)\) None 0 1
3024.1.o \(\chi_{3024}(3023, \cdot)\) 3024.1.o.a 2 1
3024.1.o.b 2
3024.1.o.c 2
3024.1.o.d 2
3024.1.u \(\chi_{3024}(1189, \cdot)\) None 0 2
3024.1.w \(\chi_{3024}(701, \cdot)\) None 0 2
3024.1.y \(\chi_{3024}(755, \cdot)\) None 0 2
3024.1.ba \(\chi_{3024}(379, \cdot)\) None 0 2
3024.1.bc \(\chi_{3024}(1223, \cdot)\) None 0 2
3024.1.bd \(\chi_{3024}(737, \cdot)\) None 0 2
3024.1.bi \(\chi_{3024}(1495, \cdot)\) None 0 2
3024.1.bj \(\chi_{3024}(577, \cdot)\) None 0 2
3024.1.bk \(\chi_{3024}(1727, \cdot)\) 3024.1.bk.a 2 2
3024.1.bk.b 2
3024.1.bk.c 2
3024.1.bk.d 2
3024.1.bl \(\chi_{3024}(809, \cdot)\) None 0 2
3024.1.bo \(\chi_{3024}(953, \cdot)\) None 0 2
3024.1.bp \(\chi_{3024}(143, \cdot)\) None 0 2
3024.1.bq \(\chi_{3024}(233, \cdot)\) None 0 2
3024.1.br \(\chi_{3024}(1007, \cdot)\) None 0 2
3024.1.bv \(\chi_{3024}(937, \cdot)\) None 0 2
3024.1.bw \(\chi_{3024}(415, \cdot)\) 3024.1.bw.a 4 2
3024.1.bx \(\chi_{3024}(73, \cdot)\) None 0 2
3024.1.by \(\chi_{3024}(127, \cdot)\) None 0 2
3024.1.cd \(\chi_{3024}(1999, \cdot)\) 3024.1.cd.a 2 2
3024.1.cd.b 2
3024.1.cd.c 2
3024.1.cd.d 2
3024.1.ce \(\chi_{3024}(649, \cdot)\) None 0 2
3024.1.cf \(\chi_{3024}(487, \cdot)\) None 0 2
3024.1.cg \(\chi_{3024}(2161, \cdot)\) 3024.1.cg.a 2 2
3024.1.cg.b 2
3024.1.cl \(\chi_{3024}(1441, \cdot)\) None 0 2
3024.1.cm \(\chi_{3024}(1927, \cdot)\) None 0 2
3024.1.cn \(\chi_{3024}(145, \cdot)\) None 0 2
3024.1.co \(\chi_{3024}(631, \cdot)\) None 0 2
3024.1.ct \(\chi_{3024}(449, \cdot)\) None 0 2
3024.1.cu \(\chi_{3024}(1655, \cdot)\) None 0 2
3024.1.cv \(\chi_{3024}(305, \cdot)\) None 0 2
3024.1.cw \(\chi_{3024}(503, \cdot)\) None 0 2
3024.1.db \(\chi_{3024}(215, \cdot)\) None 0 2
3024.1.dc \(\chi_{3024}(2321, \cdot)\) 3024.1.dc.a 2 2
3024.1.dc.b 2
3024.1.dc.c 4
3024.1.dd \(\chi_{3024}(1423, \cdot)\) 3024.1.dd.a 4 2
3024.1.de \(\chi_{3024}(2089, \cdot)\) None 0 2
3024.1.di \(\chi_{3024}(1151, \cdot)\) None 0 2
3024.1.dj \(\chi_{3024}(2249, \cdot)\) None 0 2
3024.1.do \(\chi_{3024}(197, \cdot)\) None 0 4
3024.1.dq \(\chi_{3024}(181, \cdot)\) None 0 4
3024.1.ds \(\chi_{3024}(395, \cdot)\) None 0 4
3024.1.dt \(\chi_{3024}(235, \cdot)\) None 0 4
3024.1.dw \(\chi_{3024}(163, \cdot)\) None 0 4
3024.1.dy \(\chi_{3024}(971, \cdot)\) None 0 4
3024.1.dz \(\chi_{3024}(899, \cdot)\) None 0 4
3024.1.ec \(\chi_{3024}(667, \cdot)\) None 0 4
3024.1.ee \(\chi_{3024}(397, \cdot)\) None 0 4
3024.1.eg \(\chi_{3024}(53, \cdot)\) 3024.1.eg.a 8 4
3024.1.eg.b 8
3024.1.eh \(\chi_{3024}(989, \cdot)\) None 0 4
3024.1.ej \(\chi_{3024}(829, \cdot)\) None 0 4
3024.1.em \(\chi_{3024}(325, \cdot)\) None 0 4
3024.1.eo \(\chi_{3024}(557, \cdot)\) None 0 4
3024.1.eq \(\chi_{3024}(883, \cdot)\) None 0 4
3024.1.es \(\chi_{3024}(251, \cdot)\) None 0 4
3024.1.et \(\chi_{3024}(241, \cdot)\) None 0 6
3024.1.ev \(\chi_{3024}(137, \cdot)\) None 0 6
3024.1.ey \(\chi_{3024}(401, \cdot)\) None 0 6
3024.1.fa \(\chi_{3024}(745, \cdot)\) None 0 6
3024.1.fc \(\chi_{3024}(583, \cdot)\) None 0 6
3024.1.fd \(\chi_{3024}(335, \cdot)\) None 0 6
3024.1.fe \(\chi_{3024}(295, \cdot)\) None 0 6
3024.1.fg \(\chi_{3024}(47, \cdot)\) None 0 6
3024.1.fh \(\chi_{3024}(311, \cdot)\) None 0 6
3024.1.fk \(\chi_{3024}(463, \cdot)\) None 0 6
3024.1.fm \(\chi_{3024}(167, \cdot)\) None 0 6
3024.1.fn \(\chi_{3024}(79, \cdot)\) None 0 6
3024.1.fq \(\chi_{3024}(313, \cdot)\) None 0 6
3024.1.fr \(\chi_{3024}(113, \cdot)\) None 0 6
3024.1.ft \(\chi_{3024}(265, \cdot)\) None 0 6
3024.1.fw \(\chi_{3024}(65, \cdot)\) None 0 6
3024.1.fx \(\chi_{3024}(473, \cdot)\) None 0 6
3024.1.ga \(\chi_{3024}(97, \cdot)\) None 0 6
3024.1.gc \(\chi_{3024}(281, \cdot)\) None 0 6
3024.1.gd \(\chi_{3024}(817, \cdot)\) None 0 6
3024.1.gf \(\chi_{3024}(655, \cdot)\) None 0 6
3024.1.gh \(\chi_{3024}(887, \cdot)\) None 0 6
3024.1.gj \(\chi_{3024}(383, \cdot)\) None 0 6
3024.1.gl \(\chi_{3024}(151, \cdot)\) None 0 6
3024.1.gn \(\chi_{3024}(149, \cdot)\) None 0 12
3024.1.go \(\chi_{3024}(229, \cdot)\) None 0 12
3024.1.gr \(\chi_{3024}(83, \cdot)\) None 0 12
3024.1.gt \(\chi_{3024}(59, \cdot)\) None 0 12
3024.1.gu \(\chi_{3024}(67, \cdot)\) None 0 12
3024.1.gw \(\chi_{3024}(43, \cdot)\) None 0 12
3024.1.gy \(\chi_{3024}(221, \cdot)\) None 0 12
3024.1.ha \(\chi_{3024}(29, \cdot)\) None 0 12
3024.1.hd \(\chi_{3024}(13, \cdot)\) None 0 12
3024.1.hf \(\chi_{3024}(61, \cdot)\) None 0 12
3024.1.hg \(\chi_{3024}(131, \cdot)\) None 0 12
3024.1.hj \(\chi_{3024}(403, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3024))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3024)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1512))\)\(^{\oplus 2}\)