Properties

Label 1872.1
Level 1872
Weight 1
Dimension 61
Nonzero newspaces 12
Newform subspaces 20
Sturm bound 193536
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 20 \)
Sturm bound: \(193536\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1872))\).

Total New Old
Modular forms 3080 507 2573
Cusp forms 392 61 331
Eisenstein series 2688 446 2242

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 49 0 12 0

Trace form

\( 61q - q^{3} + 2q^{5} + 4q^{7} - 7q^{9} + O(q^{10}) \) \( 61q - q^{3} + 2q^{5} + 4q^{7} - 7q^{9} + 2q^{11} + 7q^{13} + 2q^{15} + 7q^{17} + 4q^{19} + 4q^{21} - 8q^{22} + 3q^{23} + 2q^{25} + 2q^{27} + 7q^{29} - 2q^{31} + 4q^{33} - 5q^{37} - q^{39} - 3q^{41} - q^{43} - 4q^{45} - 4q^{47} + 11q^{49} - 3q^{51} + 8q^{52} - 4q^{53} - 12q^{55} + 2q^{57} - 2q^{59} - 16q^{61} + 2q^{63} - q^{65} + 8q^{67} - 9q^{69} + 8q^{73} - 2q^{75} + 5q^{79} - 7q^{81} - 5q^{85} + 8q^{88} - 4q^{89} - 6q^{91} + 2q^{93} + 10q^{97} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1872))\)

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
1872.1.b \(\chi_{1872}(233, \cdot)\) None 0 1
1872.1.e \(\chi_{1872}(1639, \cdot)\) None 0 1
1872.1.f \(\chi_{1872}(1457, \cdot)\) None 0 1
1872.1.i \(\chi_{1872}(415, \cdot)\) 1872.1.i.a 1 1
1872.1.i.b 1
1872.1.i.c 1
1872.1.k \(\chi_{1872}(703, \cdot)\) None 0 1
1872.1.l \(\chi_{1872}(1169, \cdot)\) None 0 1
1872.1.o \(\chi_{1872}(1351, \cdot)\) None 0 1
1872.1.p \(\chi_{1872}(521, \cdot)\) None 0 1
1872.1.v \(\chi_{1872}(395, \cdot)\) None 0 2
1872.1.w \(\chi_{1872}(109, \cdot)\) None 0 2
1872.1.z \(\chi_{1872}(53, \cdot)\) None 0 2
1872.1.bb \(\chi_{1872}(883, \cdot)\) 1872.1.bb.a 8 2
1872.1.bc \(\chi_{1872}(73, \cdot)\) None 0 2
1872.1.bd \(\chi_{1872}(577, \cdot)\) 1872.1.bd.a 2 2
1872.1.bg \(\chi_{1872}(863, \cdot)\) 1872.1.bg.a 4 2
1872.1.bh \(\chi_{1872}(359, \cdot)\) None 0 2
1872.1.bl \(\chi_{1872}(701, \cdot)\) None 0 2
1872.1.bn \(\chi_{1872}(235, \cdot)\) None 0 2
1872.1.bo \(\chi_{1872}(541, \cdot)\) None 0 2
1872.1.br \(\chi_{1872}(827, \cdot)\) None 0 2
1872.1.bs \(\chi_{1872}(127, \cdot)\) 1872.1.bs.a 2 2
1872.1.bs.b 2
1872.1.bs.c 2
1872.1.bv \(\chi_{1872}(737, \cdot)\) 1872.1.bv.a 4 2
1872.1.bw \(\chi_{1872}(55, \cdot)\) None 0 2
1872.1.bz \(\chi_{1872}(953, \cdot)\) None 0 2
1872.1.cb \(\chi_{1872}(257, \cdot)\) None 0 2
1872.1.cc \(\chi_{1872}(1231, \cdot)\) None 0 2
1872.1.ce \(\chi_{1872}(439, \cdot)\) None 0 2
1872.1.cg \(\chi_{1872}(1145, \cdot)\) None 0 2
1872.1.ci \(\chi_{1872}(103, \cdot)\) None 0 2
1872.1.cj \(\chi_{1872}(1049, \cdot)\) None 0 2
1872.1.ck \(\chi_{1872}(367, \cdot)\) None 0 2
1872.1.cm \(\chi_{1872}(545, \cdot)\) 1872.1.cm.a 2 2
1872.1.cp \(\chi_{1872}(79, \cdot)\) None 0 2
1872.1.cr \(\chi_{1872}(1265, \cdot)\) None 0 2
1872.1.cs \(\chi_{1872}(185, \cdot)\) None 0 2
1872.1.ct \(\chi_{1872}(1447, \cdot)\) None 0 2
1872.1.cv \(\chi_{1872}(295, \cdot)\) None 0 2
1872.1.cy \(\chi_{1872}(1193, \cdot)\) None 0 2
1872.1.da \(\chi_{1872}(113, \cdot)\) None 0 2
1872.1.dc \(\chi_{1872}(1039, \cdot)\) 1872.1.dc.a 2 2
1872.1.dc.b 2
1872.1.dd \(\chi_{1872}(209, \cdot)\) None 0 2
1872.1.df \(\chi_{1872}(1375, \cdot)\) None 0 2
1872.1.di \(\chi_{1872}(329, \cdot)\) None 0 2
1872.1.dk \(\chi_{1872}(391, \cdot)\) None 0 2
1872.1.dl \(\chi_{1872}(857, \cdot)\) None 0 2
1872.1.dn \(\chi_{1872}(1303, \cdot)\) None 0 2
1872.1.dp \(\chi_{1872}(511, \cdot)\) None 0 2
1872.1.ds \(\chi_{1872}(1121, \cdot)\) None 0 2
1872.1.dt \(\chi_{1872}(809, \cdot)\) None 0 2
1872.1.du \(\chi_{1872}(199, \cdot)\) None 0 2
1872.1.dx \(\chi_{1872}(17, \cdot)\) None 0 2
1872.1.dy \(\chi_{1872}(991, \cdot)\) 1872.1.dy.a 2 2
1872.1.dy.b 2
1872.1.dy.c 4
1872.1.eb \(\chi_{1872}(37, \cdot)\) None 0 4
1872.1.ec \(\chi_{1872}(323, \cdot)\) None 0 4
1872.1.ef \(\chi_{1872}(349, \cdot)\) None 0 4
1872.1.eh \(\chi_{1872}(227, \cdot)\) None 0 4
1872.1.ej \(\chi_{1872}(83, \cdot)\) None 0 4
1872.1.ek \(\chi_{1872}(421, \cdot)\) None 0 4
1872.1.em \(\chi_{1872}(565, \cdot)\) None 0 4
1872.1.eo \(\chi_{1872}(11, \cdot)\) None 0 4
1872.1.er \(\chi_{1872}(43, \cdot)\) None 0 4
1872.1.et \(\chi_{1872}(653, \cdot)\) None 0 4
1872.1.eu \(\chi_{1872}(77, \cdot)\) None 0 4
1872.1.ew \(\chi_{1872}(451, \cdot)\) None 0 4
1872.1.ex \(\chi_{1872}(139, \cdot)\) None 0 4
1872.1.fa \(\chi_{1872}(413, \cdot)\) None 0 4
1872.1.fb \(\chi_{1872}(101, \cdot)\) None 0 4
1872.1.fe \(\chi_{1872}(547, \cdot)\) None 0 4
1872.1.fi \(\chi_{1872}(385, \cdot)\) 1872.1.fi.a 4 4
1872.1.fi.b 4
1872.1.fj \(\chi_{1872}(265, \cdot)\) None 0 4
1872.1.fk \(\chi_{1872}(167, \cdot)\) None 0 4
1872.1.fl \(\chi_{1872}(1103, \cdot)\) None 0 4
1872.1.fq \(\chi_{1872}(71, \cdot)\) None 0 4
1872.1.fr \(\chi_{1872}(431, \cdot)\) 1872.1.fr.a 8 4
1872.1.fs \(\chi_{1872}(383, \cdot)\) None 0 4
1872.1.ft \(\chi_{1872}(119, \cdot)\) None 0 4
1872.1.fw \(\chi_{1872}(97, \cdot)\) None 0 4
1872.1.fx \(\chi_{1872}(1033, \cdot)\) None 0 4
1872.1.gc \(\chi_{1872}(145, \cdot)\) 1872.1.gc.a 4 4
1872.1.gd \(\chi_{1872}(505, \cdot)\) None 0 4
1872.1.ge \(\chi_{1872}(409, \cdot)\) None 0 4
1872.1.gf \(\chi_{1872}(817, \cdot)\) None 0 4
1872.1.gk \(\chi_{1872}(551, \cdot)\) None 0 4
1872.1.gl \(\chi_{1872}(47, \cdot)\) None 0 4
1872.1.gm \(\chi_{1872}(365, \cdot)\) None 0 4
1872.1.go \(\chi_{1872}(595, \cdot)\) None 0 4
1872.1.gp \(\chi_{1872}(355, \cdot)\) None 0 4
1872.1.gs \(\chi_{1872}(269, \cdot)\) None 0 4
1872.1.gt \(\chi_{1872}(29, \cdot)\) None 0 4
1872.1.gw \(\chi_{1872}(259, \cdot)\) None 0 4
1872.1.gz \(\chi_{1872}(211, \cdot)\) None 0 4
1872.1.hb \(\chi_{1872}(173, \cdot)\) None 0 4
1872.1.hc \(\chi_{1872}(587, \cdot)\) None 0 4
1872.1.he \(\chi_{1872}(229, \cdot)\) None 0 4
1872.1.hg \(\chi_{1872}(301, \cdot)\) None 0 4
1872.1.hj \(\chi_{1872}(371, \cdot)\) None 0 4
1872.1.hl \(\chi_{1872}(515, \cdot)\) None 0 4
1872.1.hn \(\chi_{1872}(85, \cdot)\) None 0 4
1872.1.ho \(\chi_{1872}(683, \cdot)\) None 0 4
1872.1.hr \(\chi_{1872}(397, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1872))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1872)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 2}\)