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Properties

Label 2255.1
Level 2255
Weight 1
Dimension 38
Nonzero newspaces 5
Newform subspaces 14
Sturm bound 403200
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2255 = 5 \cdot 11 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 14 \)
Sturm bound: \(403200\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2255))\).

Total New Old
Modular forms 3252 2146 1106
Cusp forms 52 38 14
Eisenstein series 3200 2108 1092

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 38 0 0 0

Trace form

\( 38 q + 14 q^{4} - 6 q^{5} + 10 q^{9} + O(q^{10}) \) \( 38 q + 14 q^{4} - 6 q^{5} + 10 q^{9} + 2 q^{11} + 10 q^{16} - 12 q^{20} + 22 q^{25} - 8 q^{31} + 6 q^{36} - 2 q^{44} - 8 q^{45} + 10 q^{49} - 2 q^{55} - 6 q^{59} + 6 q^{64} - 8 q^{66} - 4 q^{71} + 10 q^{79} - 14 q^{80} + 10 q^{81} - 8 q^{86} + 4 q^{89} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2255))\)

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
2255.1.c \(\chi_{2255}(901, \cdot)\) None 0 1
2255.1.d \(\chi_{2255}(1231, \cdot)\) None 0 1
2255.1.g \(\chi_{2255}(329, \cdot)\) None 0 1
2255.1.h \(\chi_{2255}(2254, \cdot)\) 2255.1.h.a 1 1
2255.1.h.b 1
2255.1.h.c 2
2255.1.h.d 2
2255.1.h.e 2
2255.1.h.f 2
2255.1.h.g 2
2255.1.h.h 2
2255.1.h.i 4
2255.1.h.j 4
2255.1.j \(\chi_{2255}(934, \cdot)\) None 0 2
2255.1.l \(\chi_{2255}(1057, \cdot)\) None 0 2
2255.1.n \(\chi_{2255}(122, \cdot)\) None 0 2
2255.1.o \(\chi_{2255}(452, \cdot)\) None 0 2
2255.1.q \(\chi_{2255}(1508, \cdot)\) None 0 2
2255.1.t \(\chi_{2255}(296, \cdot)\) None 0 2
2255.1.ba \(\chi_{2255}(1022, \cdot)\) None 0 4
2255.1.bd \(\chi_{2255}(694, \cdot)\) None 0 4
2255.1.be \(\chi_{2255}(331, \cdot)\) None 0 4
2255.1.bg \(\chi_{2255}(208, \cdot)\) None 0 4
2255.1.bj \(\chi_{2255}(1656, \cdot)\) None 0 4
2255.1.bk \(\chi_{2255}(646, \cdot)\) None 0 4
2255.1.bm \(\chi_{2255}(549, \cdot)\) None 0 4
2255.1.bo \(\chi_{2255}(1009, \cdot)\) 2255.1.bo.a 4 4
2255.1.bp \(\chi_{2255}(679, \cdot)\) 2255.1.bp.a 4 4
2255.1.bq \(\chi_{2255}(204, \cdot)\) None 0 4
2255.1.br \(\chi_{2255}(189, \cdot)\) None 0 4
2255.1.bs \(\chi_{2255}(734, \cdot)\) None 0 4
2255.1.bv \(\chi_{2255}(534, \cdot)\) None 0 4
2255.1.bw \(\chi_{2255}(139, \cdot)\) 2255.1.bw.a 4 4
2255.1.bz \(\chi_{2255}(469, \cdot)\) 2255.1.bz.a 4 4
2255.1.ca \(\chi_{2255}(769, \cdot)\) None 0 4
2255.1.cb \(\chi_{2255}(351, \cdot)\) None 0 4
2255.1.ce \(\chi_{2255}(51, \cdot)\) None 0 4
2255.1.cf \(\chi_{2255}(426, \cdot)\) None 0 4
2255.1.ci \(\chi_{2255}(666, \cdot)\) None 0 4
2255.1.cj \(\chi_{2255}(206, \cdot)\) None 0 4
2255.1.cm \(\chi_{2255}(491, \cdot)\) None 0 4
2255.1.cn \(\chi_{2255}(271, \cdot)\) None 0 4
2255.1.cq \(\chi_{2255}(1911, \cdot)\) None 0 4
2255.1.cr \(\chi_{2255}(556, \cdot)\) None 0 4
2255.1.cu \(\chi_{2255}(406, \cdot)\) None 0 4
2255.1.cv \(\chi_{2255}(414, \cdot)\) None 0 4
2255.1.cw \(\chi_{2255}(754, \cdot)\) None 0 4
2255.1.cy \(\chi_{2255}(74, \cdot)\) None 0 8
2255.1.da \(\chi_{2255}(21, \cdot)\) None 0 8
2255.1.dc \(\chi_{2255}(46, \cdot)\) None 0 8
2255.1.df \(\chi_{2255}(266, \cdot)\) None 0 8
2255.1.dg \(\chi_{2255}(156, \cdot)\) None 0 8
2255.1.dj \(\chi_{2255}(501, \cdot)\) None 0 8
2255.1.dk \(\chi_{2255}(408, \cdot)\) None 0 8
2255.1.dn \(\chi_{2255}(323, \cdot)\) None 0 8
2255.1.do \(\chi_{2255}(267, \cdot)\) None 0 8
2255.1.ds \(\chi_{2255}(278, \cdot)\) None 0 8
2255.1.dt \(\chi_{2255}(702, \cdot)\) None 0 8
2255.1.du \(\chi_{2255}(863, \cdot)\) None 0 8
2255.1.dx \(\chi_{2255}(37, \cdot)\) None 0 8
2255.1.dy \(\chi_{2255}(113, \cdot)\) None 0 8
2255.1.ea \(\chi_{2255}(168, \cdot)\) None 0 8
2255.1.ec \(\chi_{2255}(78, \cdot)\) None 0 8
2255.1.eh \(\chi_{2255}(223, \cdot)\) None 0 8
2255.1.ei \(\chi_{2255}(1412, \cdot)\) None 0 8
2255.1.ej \(\chi_{2255}(42, \cdot)\) None 0 8
2255.1.el \(\chi_{2255}(23, \cdot)\) None 0 8
2255.1.em \(\chi_{2255}(433, \cdot)\) None 0 8
2255.1.en \(\chi_{2255}(163, \cdot)\) None 0 8
2255.1.eo \(\chi_{2255}(312, \cdot)\) None 0 8
2255.1.et \(\chi_{2255}(92, \cdot)\) None 0 8
2255.1.eu \(\chi_{2255}(207, \cdot)\) None 0 8
2255.1.ex \(\chi_{2255}(203, \cdot)\) None 0 8
2255.1.ey \(\chi_{2255}(103, \cdot)\) None 0 8
2255.1.ez \(\chi_{2255}(378, \cdot)\) None 0 8
2255.1.fd \(\chi_{2255}(102, \cdot)\) None 0 8
2255.1.ff \(\chi_{2255}(1068, \cdot)\) None 0 8
2255.1.fg \(\chi_{2255}(494, \cdot)\) None 0 8
2255.1.fj \(\chi_{2255}(39, \cdot)\) None 0 8
2255.1.fk \(\chi_{2255}(84, \cdot)\) None 0 8
2255.1.fn \(\chi_{2255}(524, \cdot)\) None 0 8
2255.1.fo \(\chi_{2255}(799, \cdot)\) None 0 8
2255.1.fq \(\chi_{2255}(61, \cdot)\) None 0 8
2255.1.ft \(\chi_{2255}(52, \cdot)\) None 0 16
2255.1.fv \(\chi_{2255}(17, \cdot)\) None 0 16
2255.1.fx \(\chi_{2255}(413, \cdot)\) None 0 16
2255.1.fy \(\chi_{2255}(28, \cdot)\) None 0 16
2255.1.gb \(\chi_{2255}(117, \cdot)\) None 0 16
2255.1.gc \(\chi_{2255}(142, \cdot)\) None 0 16
2255.1.gf \(\chi_{2255}(26, \cdot)\) None 0 16
2255.1.gg \(\chi_{2255}(104, \cdot)\) None 0 16
2255.1.gi \(\chi_{2255}(69, \cdot)\) None 0 16
2255.1.gk \(\chi_{2255}(126, \cdot)\) None 0 16
2255.1.go \(\chi_{2255}(136, \cdot)\) None 0 16
2255.1.gp \(\chi_{2255}(306, \cdot)\) None 0 16
2255.1.gq \(\chi_{2255}(56, \cdot)\) None 0 16
2255.1.gt \(\chi_{2255}(34, \cdot)\) None 0 16
2255.1.gu \(\chi_{2255}(229, \cdot)\) None 0 16
2255.1.gv \(\chi_{2255}(179, \cdot)\) None 0 16
2255.1.gz \(\chi_{2255}(14, \cdot)\) None 0 16
2255.1.hb \(\chi_{2255}(71, \cdot)\) None 0 16
2255.1.hd \(\chi_{2255}(7, \cdot)\) None 0 16
2255.1.he \(\chi_{2255}(217, \cdot)\) None 0 16
2255.1.hh \(\chi_{2255}(263, \cdot)\) None 0 16
2255.1.hi \(\chi_{2255}(63, \cdot)\) None 0 16
2255.1.hl \(\chi_{2255}(68, \cdot)\) None 0 16
2255.1.hn \(\chi_{2255}(13, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2255))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2255)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(451))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2255))\)\(^{\oplus 1}\)