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Properties

Label 2565.1
Level 2565
Weight 1
Dimension 132
Nonzero newspaces 7
Newform subspaces 21
Sturm bound 466560
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2565 = 3^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 21 \)
Sturm bound: \(466560\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2565))\).

Total New Old
Modular forms 4710 1764 2946
Cusp forms 390 132 258
Eisenstein series 4320 1632 2688

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 132 0 0 0

Trace form

\( 132 q - 8 q^{4} + 4 q^{10} - 4 q^{16} + 2 q^{19} - 12 q^{25} + 16 q^{26} - 24 q^{30} + 4 q^{31} - 4 q^{34} - 4 q^{40} - 8 q^{44} - 4 q^{46} - 12 q^{49} + 4 q^{61} - 12 q^{64} + 48 q^{66} + 4 q^{79} + 16 q^{80}+ \cdots - 24 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2565))\)

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
2565.1.d \(\chi_{2565}(2186, \cdot)\) None 0 1
2565.1.e \(\chi_{2565}(2431, \cdot)\) None 0 1
2565.1.f \(\chi_{2565}(134, \cdot)\) None 0 1
2565.1.g \(\chi_{2565}(379, \cdot)\) 2565.1.g.a 4 1
2565.1.m \(\chi_{2565}(512, \cdot)\) None 0 2
2565.1.o \(\chi_{2565}(1027, \cdot)\) None 0 2
2565.1.q \(\chi_{2565}(316, \cdot)\) None 0 2
2565.1.r \(\chi_{2565}(1151, \cdot)\) None 0 2
2565.1.u \(\chi_{2565}(539, \cdot)\) 2565.1.u.a 2 2
2565.1.u.b 2
2565.1.u.c 2
2565.1.u.d 2
2565.1.v \(\chi_{2565}(2269, \cdot)\) 2565.1.v.a 4 2
2565.1.v.b 4
2565.1.y \(\chi_{2565}(559, \cdot)\) None 0 2
2565.1.z \(\chi_{2565}(1234, \cdot)\) 2565.1.z.a 2 2
2565.1.z.b 2
2565.1.z.c 4
2565.1.z.d 8
2565.1.ba \(\chi_{2565}(1394, \cdot)\) None 0 2
2565.1.bb \(\chi_{2565}(989, \cdot)\) None 0 2
2565.1.bf \(\chi_{2565}(46, \cdot)\) None 0 2
2565.1.bg \(\chi_{2565}(721, \cdot)\) None 0 2
2565.1.bh \(\chi_{2565}(881, \cdot)\) None 0 2
2565.1.bi \(\chi_{2565}(476, \cdot)\) None 0 2
2565.1.bn \(\chi_{2565}(26, \cdot)\) None 0 2
2565.1.bo \(\chi_{2565}(1756, \cdot)\) None 0 2
2565.1.bq \(\chi_{2565}(829, \cdot)\) None 0 2
2565.1.br \(\chi_{2565}(1664, \cdot)\) None 0 2
2565.1.cf \(\chi_{2565}(748, \cdot)\) None 0 4
2565.1.ch \(\chi_{2565}(278, \cdot)\) None 0 4
2565.1.cj \(\chi_{2565}(107, \cdot)\) None 0 4
2565.1.ck \(\chi_{2565}(577, \cdot)\) None 0 4
2565.1.cm \(\chi_{2565}(172, \cdot)\) None 0 4
2565.1.co \(\chi_{2565}(8, \cdot)\) None 0 4
2565.1.cq \(\chi_{2565}(683, \cdot)\) None 0 4
2565.1.ct \(\chi_{2565}(163, \cdot)\) None 0 4
2565.1.cu \(\chi_{2565}(491, \cdot)\) None 0 6
2565.1.cx \(\chi_{2565}(166, \cdot)\) None 0 6
2565.1.cy \(\chi_{2565}(389, \cdot)\) None 0 6
2565.1.da \(\chi_{2565}(364, \cdot)\) None 0 6
2565.1.db \(\chi_{2565}(149, \cdot)\) None 0 6
2565.1.dd \(\chi_{2565}(124, \cdot)\) None 0 6
2565.1.de \(\chi_{2565}(154, \cdot)\) None 0 6
2565.1.df \(\chi_{2565}(44, \cdot)\) None 0 6
2565.1.dk \(\chi_{2565}(206, \cdot)\) None 0 6
2565.1.dl \(\chi_{2565}(136, \cdot)\) None 0 6
2565.1.dm \(\chi_{2565}(161, \cdot)\) None 0 6
2565.1.dn \(\chi_{2565}(181, \cdot)\) None 0 6
2565.1.do \(\chi_{2565}(79, \cdot)\) None 0 6
2565.1.dp \(\chi_{2565}(74, \cdot)\) None 0 6
2565.1.dt \(\chi_{2565}(544, \cdot)\) None 0 6
2565.1.du \(\chi_{2565}(419, \cdot)\) None 0 6
2565.1.dv \(\chi_{2565}(239, \cdot)\) None 0 6
2565.1.dy \(\chi_{2565}(94, \cdot)\) 2565.1.dy.a 6 6
2565.1.dy.b 6
2565.1.dy.c 12
2565.1.dy.d 24
2565.1.dz \(\chi_{2565}(259, \cdot)\) None 0 6
2565.1.ea \(\chi_{2565}(524, \cdot)\) None 0 6
2565.1.eb \(\chi_{2565}(329, \cdot)\) None 0 6
2565.1.ec \(\chi_{2565}(1174, \cdot)\) None 0 6
2565.1.ed \(\chi_{2565}(929, \cdot)\) None 0 6
2565.1.ee \(\chi_{2565}(184, \cdot)\) None 0 6
2565.1.eg \(\chi_{2565}(1526, \cdot)\) None 0 6
2565.1.eh \(\chi_{2565}(526, \cdot)\) None 0 6
2565.1.em \(\chi_{2565}(11, \cdot)\) None 0 6
2565.1.eq \(\chi_{2565}(601, \cdot)\) None 0 6
2565.1.er \(\chi_{2565}(151, \cdot)\) None 0 6
2565.1.es \(\chi_{2565}(581, \cdot)\) None 0 6
2565.1.et \(\chi_{2565}(191, \cdot)\) None 0 6
2565.1.ex \(\chi_{2565}(31, \cdot)\) None 0 6
2565.1.ey \(\chi_{2565}(421, \cdot)\) None 0 6
2565.1.ez \(\chi_{2565}(416, \cdot)\) None 0 6
2565.1.fa \(\chi_{2565}(661, \cdot)\) None 0 6
2565.1.fb \(\chi_{2565}(446, \cdot)\) None 0 6
2565.1.fe \(\chi_{2565}(719, \cdot)\) None 0 6
2565.1.ff \(\chi_{2565}(109, \cdot)\) 2565.1.ff.a 12 6
2565.1.ff.b 12
2565.1.fg \(\chi_{2565}(404, \cdot)\) 2565.1.fg.a 6 6
2565.1.fg.b 6
2565.1.fg.c 6
2565.1.fg.d 6
2565.1.fh \(\chi_{2565}(694, \cdot)\) None 0 6
2565.1.fn \(\chi_{2565}(91, \cdot)\) None 0 6
2565.1.fo \(\chi_{2565}(1016, \cdot)\) None 0 6
2565.1.fp \(\chi_{2565}(211, \cdot)\) None 0 6
2565.1.fs \(\chi_{2565}(131, \cdot)\) None 0 6
2565.1.ft \(\chi_{2565}(241, \cdot)\) None 0 6
2565.1.fw \(\chi_{2565}(101, \cdot)\) None 0 6
2565.1.fx \(\chi_{2565}(34, \cdot)\) None 0 6
2565.1.fz \(\chi_{2565}(479, \cdot)\) None 0 6
2565.1.gb \(\chi_{2565}(283, \cdot)\) None 0 12
2565.1.gc \(\chi_{2565}(383, \cdot)\) None 0 12
2565.1.ge \(\chi_{2565}(98, \cdot)\) None 0 12
2565.1.gg \(\chi_{2565}(73, \cdot)\) None 0 12
2565.1.gh \(\chi_{2565}(28, \cdot)\) None 0 12
2565.1.gk \(\chi_{2565}(43, \cdot)\) None 0 12
2565.1.gl \(\chi_{2565}(167, \cdot)\) None 0 12
2565.1.gs \(\chi_{2565}(113, \cdot)\) None 0 12
2565.1.gt \(\chi_{2565}(392, \cdot)\) None 0 12
2565.1.gv \(\chi_{2565}(122, \cdot)\) None 0 12
2565.1.gw \(\chi_{2565}(7, \cdot)\) None 0 12
2565.1.gy \(\chi_{2565}(58, \cdot)\) None 0 12
2565.1.gz \(\chi_{2565}(277, \cdot)\) None 0 12
2565.1.hc \(\chi_{2565}(517, \cdot)\) None 0 12
2565.1.hd \(\chi_{2565}(358, \cdot)\) None 0 12
2565.1.he \(\chi_{2565}(2, \cdot)\) None 0 12
2565.1.hf \(\chi_{2565}(173, \cdot)\) None 0 12
2565.1.hk \(\chi_{2565}(413, \cdot)\) None 0 12
2565.1.hl \(\chi_{2565}(53, \cdot)\) None 0 12
2565.1.hn \(\chi_{2565}(442, \cdot)\) None 0 12
2565.1.hq \(\chi_{2565}(313, \cdot)\) None 0 12
2565.1.hr \(\chi_{2565}(112, \cdot)\) None 0 12
2565.1.hs \(\chi_{2565}(488, \cdot)\) None 0 12
2565.1.ht \(\chi_{2565}(212, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2565))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2565)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(513))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 2}\)