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Properties

Label 1365.1
Level 1365
Weight 1
Dimension 32
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 129024
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1365 = 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(129024\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1365))\).

Total New Old
Modular forms 2440 688 1752
Cusp forms 136 32 104
Eisenstein series 2304 656 1648

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 32 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{25} + 20 q^{36} + 8 q^{49} + 4 q^{51} - 8 q^{55} - 8 q^{61} + 8 q^{64} - 8 q^{69} + 4 q^{79} - 16 q^{81} - 24 q^{85} + 8 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1365))\)

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
1365.1.b \(\chi_{1365}(911, \cdot)\) None 0 1
1365.1.c \(\chi_{1365}(181, \cdot)\) None 0 1
1365.1.h \(\chi_{1365}(664, \cdot)\) None 0 1
1365.1.i \(\chi_{1365}(974, \cdot)\) None 0 1
1365.1.l \(\chi_{1365}(454, \cdot)\) None 0 1
1365.1.m \(\chi_{1365}(1184, \cdot)\) None 0 1
1365.1.n \(\chi_{1365}(701, \cdot)\) None 0 1
1365.1.o \(\chi_{1365}(391, \cdot)\) None 0 1
1365.1.u \(\chi_{1365}(307, \cdot)\) None 0 2
1365.1.x \(\chi_{1365}(8, \cdot)\) None 0 2
1365.1.ba \(\chi_{1365}(337, \cdot)\) None 0 2
1365.1.bb \(\chi_{1365}(482, \cdot)\) None 0 2
1365.1.be \(\chi_{1365}(421, \cdot)\) None 0 2
1365.1.bf \(\chi_{1365}(356, \cdot)\) None 0 2
1365.1.bg \(\chi_{1365}(629, \cdot)\) 1365.1.bg.a 4 2
1365.1.bg.b 4
1365.1.bh \(\chi_{1365}(694, \cdot)\) None 0 2
1365.1.bk \(\chi_{1365}(547, \cdot)\) None 0 2
1365.1.bl \(\chi_{1365}(272, \cdot)\) None 0 2
1365.1.bp \(\chi_{1365}(853, \cdot)\) None 0 2
1365.1.bq \(\chi_{1365}(827, \cdot)\) None 0 2
1365.1.bu \(\chi_{1365}(724, \cdot)\) None 0 2
1365.1.bv \(\chi_{1365}(569, \cdot)\) None 0 2
1365.1.bw \(\chi_{1365}(926, \cdot)\) None 0 2
1365.1.bx \(\chi_{1365}(166, \cdot)\) None 0 2
1365.1.ca \(\chi_{1365}(464, \cdot)\) None 0 2
1365.1.cb \(\chi_{1365}(829, \cdot)\) None 0 2
1365.1.cg \(\chi_{1365}(601, \cdot)\) None 0 2
1365.1.ch \(\chi_{1365}(491, \cdot)\) None 0 2
1365.1.ci \(\chi_{1365}(586, \cdot)\) None 0 2
1365.1.cj \(\chi_{1365}(116, \cdot)\) None 0 2
1365.1.ck \(\chi_{1365}(599, \cdot)\) None 0 2
1365.1.cl \(\chi_{1365}(649, \cdot)\) None 0 2
1365.1.cm \(\chi_{1365}(29, \cdot)\) None 0 2
1365.1.cn \(\chi_{1365}(244, \cdot)\) None 0 2
1365.1.ct \(\chi_{1365}(61, \cdot)\) None 0 2
1365.1.cu \(\chi_{1365}(1031, \cdot)\) None 0 2
1365.1.cx \(\chi_{1365}(556, \cdot)\) None 0 2
1365.1.cy \(\chi_{1365}(191, \cdot)\) None 0 2
1365.1.cz \(\chi_{1365}(389, \cdot)\) 1365.1.cz.a 2 2
1365.1.cz.b 2
1365.1.cz.c 2
1365.1.cz.d 2
1365.1.da \(\chi_{1365}(859, \cdot)\) None 0 2
1365.1.db \(\chi_{1365}(134, \cdot)\) None 0 2
1365.1.dc \(\chi_{1365}(139, \cdot)\) None 0 2
1365.1.dl \(\chi_{1365}(706, \cdot)\) None 0 2
1365.1.dm \(\chi_{1365}(386, \cdot)\) None 0 2
1365.1.dn \(\chi_{1365}(376, \cdot)\) None 0 2
1365.1.do \(\chi_{1365}(326, \cdot)\) None 0 2
1365.1.dp \(\chi_{1365}(179, \cdot)\) None 0 2
1365.1.dq \(\chi_{1365}(94, \cdot)\) None 0 2
1365.1.dt \(\chi_{1365}(296, \cdot)\) None 0 2
1365.1.du \(\chi_{1365}(451, \cdot)\) None 0 2
1365.1.dy \(\chi_{1365}(199, \cdot)\) None 0 2
1365.1.dz \(\chi_{1365}(74, \cdot)\) None 0 2
1365.1.ea \(\chi_{1365}(2, \cdot)\) None 0 4
1365.1.ed \(\chi_{1365}(418, \cdot)\) None 0 4
1365.1.ee \(\chi_{1365}(73, \cdot)\) None 0 4
1365.1.eg \(\chi_{1365}(722, \cdot)\) None 0 4
1365.1.ei \(\chi_{1365}(158, \cdot)\) None 0 4
1365.1.el \(\chi_{1365}(262, \cdot)\) None 0 4
1365.1.en \(\chi_{1365}(97, \cdot)\) None 0 4
1365.1.ep \(\chi_{1365}(242, \cdot)\) None 0 4
1365.1.es \(\chi_{1365}(17, \cdot)\) None 0 4
1365.1.et \(\chi_{1365}(562, \cdot)\) None 0 4
1365.1.eu \(\chi_{1365}(46, \cdot)\) None 0 4
1365.1.ev \(\chi_{1365}(236, \cdot)\) None 0 4
1365.1.fa \(\chi_{1365}(59, \cdot)\) None 0 4
1365.1.fb \(\chi_{1365}(184, \cdot)\) None 0 4
1365.1.fc \(\chi_{1365}(68, \cdot)\) None 0 4
1365.1.fd \(\chi_{1365}(277, \cdot)\) None 0 4
1365.1.fi \(\chi_{1365}(152, \cdot)\) None 0 4
1365.1.fj \(\chi_{1365}(88, \cdot)\) None 0 4
1365.1.fo \(\chi_{1365}(352, \cdot)\) None 0 4
1365.1.fp \(\chi_{1365}(62, \cdot)\) None 0 4
1365.1.fq \(\chi_{1365}(22, \cdot)\) None 0 4
1365.1.fr \(\chi_{1365}(38, \cdot)\) None 0 4
1365.1.fs \(\chi_{1365}(109, \cdot)\) None 0 4
1365.1.ft \(\chi_{1365}(164, \cdot)\) None 0 4
1365.1.fy \(\chi_{1365}(604, \cdot)\) None 0 4
1365.1.fz \(\chi_{1365}(379, \cdot)\) None 0 4
1365.1.ga \(\chi_{1365}(479, \cdot)\) None 0 4
1365.1.gb \(\chi_{1365}(314, \cdot)\) 1365.1.gb.a 8 4
1365.1.gb.b 8
1365.1.gg \(\chi_{1365}(41, \cdot)\) None 0 4
1365.1.gh \(\chi_{1365}(206, \cdot)\) None 0 4
1365.1.gi \(\chi_{1365}(106, \cdot)\) None 0 4
1365.1.gj \(\chi_{1365}(331, \cdot)\) None 0 4
1365.1.go \(\chi_{1365}(551, \cdot)\) None 0 4
1365.1.gp \(\chi_{1365}(151, \cdot)\) None 0 4
1365.1.gq \(\chi_{1365}(142, \cdot)\) None 0 4
1365.1.gr \(\chi_{1365}(503, \cdot)\) None 0 4
1365.1.gs \(\chi_{1365}(43, \cdot)\) None 0 4
1365.1.gt \(\chi_{1365}(248, \cdot)\) None 0 4
1365.1.gy \(\chi_{1365}(173, \cdot)\) None 0 4
1365.1.gz \(\chi_{1365}(172, \cdot)\) None 0 4
1365.1.hd \(\chi_{1365}(502, \cdot)\) None 0 4
1365.1.hf \(\chi_{1365}(422, \cdot)\) None 0 4
1365.1.hh \(\chi_{1365}(197, \cdot)\) None 0 4
1365.1.hi \(\chi_{1365}(202, \cdot)\) None 0 4
1365.1.hk \(\chi_{1365}(397, \cdot)\) None 0 4
1365.1.hm \(\chi_{1365}(317, \cdot)\) None 0 4
1365.1.hp \(\chi_{1365}(137, \cdot)\) None 0 4
1365.1.hq \(\chi_{1365}(682, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1365))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1365)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(455))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1365))\)\(^{\oplus 1}\)