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Properties

Label 2736.1
Level 2736
Weight 1
Dimension 44
Nonzero newspaces 7
Newform subspaces 12
Sturm bound 414720
Trace bound 13

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Defining parameters

Level: \( N \) = \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 12 \)
Sturm bound: \(414720\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2736))\).

Total New Old
Modular forms 4668 733 3935
Cusp forms 636 44 592
Eisenstein series 4032 689 3343

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 4 0 0

Trace form

\( 44 q - q^{5} + q^{7} - 4 q^{9} + O(q^{10}) \) \( 44 q - q^{5} + q^{7} - 4 q^{9} - 3 q^{11} + 4 q^{13} + q^{17} + q^{19} - 6 q^{25} - 3 q^{35} - 4 q^{37} + 2 q^{39} + 5 q^{43} + 2 q^{45} + q^{47} - 14 q^{49} + 9 q^{55} - 4 q^{57} + 8 q^{61} - 2 q^{63} + q^{73} + q^{77} + 9 q^{79} + 4 q^{81} - 5 q^{85} - 2 q^{87} + 9 q^{91} + 2 q^{93} - q^{95} + 4 q^{97} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2736))\)

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
2736.1.b \(\chi_{2736}(2735, \cdot)\) 2736.1.b.a 4 1
2736.1.b.b 8
2736.1.c \(\chi_{2736}(343, \cdot)\) None 0 1
2736.1.h \(\chi_{2736}(305, \cdot)\) None 0 1
2736.1.i \(\chi_{2736}(2089, \cdot)\) None 0 1
2736.1.l \(\chi_{2736}(1367, \cdot)\) None 0 1
2736.1.m \(\chi_{2736}(1711, \cdot)\) None 0 1
2736.1.n \(\chi_{2736}(1673, \cdot)\) None 0 1
2736.1.o \(\chi_{2736}(721, \cdot)\) 2736.1.o.a 1 1
2736.1.o.b 1
2736.1.o.c 2
2736.1.v \(\chi_{2736}(989, \cdot)\) None 0 2
2736.1.w \(\chi_{2736}(37, \cdot)\) None 0 2
2736.1.z \(\chi_{2736}(683, \cdot)\) None 0 2
2736.1.ba \(\chi_{2736}(1027, \cdot)\) None 0 2
2736.1.bc \(\chi_{2736}(2041, \cdot)\) None 0 2
2736.1.bd \(\chi_{2736}(353, \cdot)\) None 0 2
2736.1.bi \(\chi_{2736}(1303, \cdot)\) None 0 2
2736.1.bj \(\chi_{2736}(1247, \cdot)\) None 0 2
2736.1.bk \(\chi_{2736}(847, \cdot)\) 2736.1.bk.a 2 2
2736.1.bk.b 2
2736.1.bl \(\chi_{2736}(791, \cdot)\) None 0 2
2736.1.bo \(\chi_{2736}(1969, \cdot)\) None 0 2
2736.1.bp \(\chi_{2736}(425, \cdot)\) None 0 2
2736.1.br \(\chi_{2736}(761, \cdot)\) None 0 2
2736.1.bs \(\chi_{2736}(1633, \cdot)\) 2736.1.bs.a 4 2
2736.1.bw \(\chi_{2736}(455, \cdot)\) None 0 2
2736.1.bx \(\chi_{2736}(799, \cdot)\) None 0 2
2736.1.ca \(\chi_{2736}(1375, \cdot)\) None 0 2
2736.1.cb \(\chi_{2736}(1319, \cdot)\) None 0 2
2736.1.cd \(\chi_{2736}(145, \cdot)\) 2736.1.cd.a 2 2
2736.1.ce \(\chi_{2736}(809, \cdot)\) None 0 2
2736.1.ch \(\chi_{2736}(919, \cdot)\) None 0 2
2736.1.ci \(\chi_{2736}(863, \cdot)\) None 0 2
2736.1.cl \(\chi_{2736}(1217, \cdot)\) None 0 2
2736.1.cm \(\chi_{2736}(265, \cdot)\) None 0 2
2736.1.cp \(\chi_{2736}(601, \cdot)\) None 0 2
2736.1.cq \(\chi_{2736}(1265, \cdot)\) None 0 2
2736.1.cr \(\chi_{2736}(7, \cdot)\) None 0 2
2736.1.cs \(\chi_{2736}(335, \cdot)\) None 0 2
2736.1.cv \(\chi_{2736}(911, \cdot)\) None 0 2
2736.1.cw \(\chi_{2736}(1255, \cdot)\) None 0 2
2736.1.cz \(\chi_{2736}(217, \cdot)\) None 0 2
2736.1.da \(\chi_{2736}(881, \cdot)\) None 0 2
2736.1.de \(\chi_{2736}(673, \cdot)\) None 0 2
2736.1.df \(\chi_{2736}(1337, \cdot)\) None 0 2
2736.1.dg \(\chi_{2736}(463, \cdot)\) None 0 2
2736.1.dh \(\chi_{2736}(407, \cdot)\) None 0 2
2736.1.dn \(\chi_{2736}(829, \cdot)\) None 0 4
2736.1.dq \(\chi_{2736}(125, \cdot)\) None 0 4
2736.1.dr \(\chi_{2736}(227, \cdot)\) None 0 4
2736.1.du \(\chi_{2736}(619, \cdot)\) None 0 4
2736.1.dw \(\chi_{2736}(691, \cdot)\) None 0 4
2736.1.dx \(\chi_{2736}(635, \cdot)\) None 0 4
2736.1.dz \(\chi_{2736}(563, \cdot)\) None 0 4
2736.1.ec \(\chi_{2736}(115, \cdot)\) None 0 4
2736.1.ed \(\chi_{2736}(77, \cdot)\) None 0 4
2736.1.eg \(\chi_{2736}(445, \cdot)\) None 0 4
2736.1.ei \(\chi_{2736}(373, \cdot)\) None 0 4
2736.1.ej \(\chi_{2736}(653, \cdot)\) None 0 4
2736.1.el \(\chi_{2736}(581, \cdot)\) None 0 4
2736.1.eo \(\chi_{2736}(493, \cdot)\) None 0 4
2736.1.ep \(\chi_{2736}(163, \cdot)\) None 0 4
2736.1.es \(\chi_{2736}(107, \cdot)\) None 0 4
2736.1.et \(\chi_{2736}(1199, \cdot)\) None 0 6
2736.1.ev \(\chi_{2736}(727, \cdot)\) None 0 6
2736.1.ey \(\chi_{2736}(167, \cdot)\) None 0 6
2736.1.fa \(\chi_{2736}(175, \cdot)\) None 0 6
2736.1.fc \(\chi_{2736}(553, \cdot)\) None 0 6
2736.1.fe \(\chi_{2736}(689, \cdot)\) None 0 6
2736.1.ff \(\chi_{2736}(233, \cdot)\) None 0 6
2736.1.fg \(\chi_{2736}(433, \cdot)\) 2736.1.fg.a 6 6
2736.1.fj \(\chi_{2736}(17, \cdot)\) None 0 6
2736.1.fl \(\chi_{2736}(649, \cdot)\) None 0 6
2736.1.fm \(\chi_{2736}(193, \cdot)\) None 0 6
2736.1.fo \(\chi_{2736}(137, \cdot)\) None 0 6
2736.1.fq \(\chi_{2736}(367, \cdot)\) None 0 6
2736.1.fs \(\chi_{2736}(743, \cdot)\) None 0 6
2736.1.ft \(\chi_{2736}(143, \cdot)\) None 0 6
2736.1.fv \(\chi_{2736}(55, \cdot)\) None 0 6
2736.1.fy \(\chi_{2736}(71, \cdot)\) None 0 6
2736.1.ga \(\chi_{2736}(271, \cdot)\) 2736.1.ga.a 6 6
2736.1.ga.b 6
2736.1.gb \(\chi_{2736}(967, \cdot)\) None 0 6
2736.1.gd \(\chi_{2736}(383, \cdot)\) None 0 6
2736.1.gf \(\chi_{2736}(329, \cdot)\) None 0 6
2736.1.gg \(\chi_{2736}(97, \cdot)\) None 0 6
2736.1.gj \(\chi_{2736}(929, \cdot)\) None 0 6
2736.1.gl \(\chi_{2736}(409, \cdot)\) None 0 6
2736.1.gn \(\chi_{2736}(245, \cdot)\) None 0 12
2736.1.gp \(\chi_{2736}(13, \cdot)\) None 0 12
2736.1.gr \(\chi_{2736}(283, \cdot)\) None 0 12
2736.1.gs \(\chi_{2736}(395, \cdot)\) None 0 12
2736.1.gu \(\chi_{2736}(595, \cdot)\) None 0 12
2736.1.gx \(\chi_{2736}(59, \cdot)\) None 0 12
2736.1.gy \(\chi_{2736}(205, \cdot)\) None 0 12
2736.1.hb \(\chi_{2736}(557, \cdot)\) None 0 12
2736.1.hd \(\chi_{2736}(109, \cdot)\) None 0 12
2736.1.he \(\chi_{2736}(5, \cdot)\) None 0 12
2736.1.hg \(\chi_{2736}(155, \cdot)\) None 0 12
2736.1.hi \(\chi_{2736}(43, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2736))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2736)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2736))\)\(^{\oplus 1}\)