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Properties

Label 2925.1
Level 2925
Weight 1
Dimension 114
Nonzero newspaces 12
Newform subspaces 20
Sturm bound 604800
Trace bound 19

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Defining parameters

Level: \( N \) = \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 20 \)
Sturm bound: \(604800\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2925))\).

Total New Old
Modular forms 5752 2144 3608
Cusp forms 376 114 262
Eisenstein series 5376 2030 3346

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 90 8 16 0

Trace form

\( 114 q + 2 q^{7} + O(q^{10}) \) \( 114 q + 2 q^{7} + 8 q^{10} + 12 q^{11} + 6 q^{16} + 2 q^{19} - 16 q^{22} - 4 q^{26} - 2 q^{28} + 6 q^{31} + 4 q^{36} - 2 q^{37} - 8 q^{40} - 12 q^{41} + 16 q^{43} + 4 q^{46} + 14 q^{52} - 4 q^{56} - 4 q^{61} + 40 q^{64} + 2 q^{67} + 20 q^{71} + 2 q^{73} + 2 q^{76} + 24 q^{81} - 24 q^{82} + 8 q^{86} + 8 q^{88} - 2 q^{91} - 40 q^{94} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2925))\)

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
2925.1.d \(\chi_{2925}(2276, \cdot)\) None 0 1
2925.1.e \(\chi_{2925}(2924, \cdot)\) None 0 1
2925.1.f \(\chi_{2925}(1574, \cdot)\) None 0 1
2925.1.g \(\chi_{2925}(701, \cdot)\) None 0 1
2925.1.m \(\chi_{2925}(593, \cdot)\) None 0 2
2925.1.o \(\chi_{2925}(532, \cdot)\) 2925.1.o.a 4 2
2925.1.o.b 8
2925.1.s \(\chi_{2925}(226, \cdot)\) 2925.1.s.a 2 2
2925.1.t \(\chi_{2925}(424, \cdot)\) 2925.1.t.a 2 2
2925.1.t.b 2
2925.1.u \(\chi_{2925}(118, \cdot)\) None 0 2
2925.1.x \(\chi_{2925}(2582, \cdot)\) None 0 2
2925.1.z \(\chi_{2925}(1751, \cdot)\) None 0 2
2925.1.ba \(\chi_{2925}(1499, \cdot)\) None 0 2
2925.1.bd \(\chi_{2925}(1076, \cdot)\) None 0 2
2925.1.be \(\chi_{2925}(74, \cdot)\) None 0 2
2925.1.bh \(\chi_{2925}(251, \cdot)\) None 0 2
2925.1.bi \(\chi_{2925}(1676, \cdot)\) 2925.1.bi.a 2 2
2925.1.bi.b 2
2925.1.bj \(\chi_{2925}(224, \cdot)\) None 0 2
2925.1.bk \(\chi_{2925}(599, \cdot)\) None 0 2
2925.1.bo \(\chi_{2925}(1349, \cdot)\) None 0 2
2925.1.bp \(\chi_{2925}(974, \cdot)\) 2925.1.bp.a 4 2
2925.1.bq \(\chi_{2925}(926, \cdot)\) None 0 2
2925.1.br \(\chi_{2925}(326, \cdot)\) None 0 2
2925.1.bw \(\chi_{2925}(374, \cdot)\) None 0 2
2925.1.bx \(\chi_{2925}(776, \cdot)\) None 0 2
2925.1.bz \(\chi_{2925}(1049, \cdot)\) None 0 2
2925.1.ca \(\chi_{2925}(101, \cdot)\) None 0 2
2925.1.cb \(\chi_{2925}(116, \cdot)\) None 0 4
2925.1.cc \(\chi_{2925}(404, \cdot)\) None 0 4
2925.1.cg \(\chi_{2925}(584, \cdot)\) None 0 4
2925.1.ch \(\chi_{2925}(521, \cdot)\) None 0 4
2925.1.cj \(\chi_{2925}(32, \cdot)\) None 0 4
2925.1.cl \(\chi_{2925}(632, \cdot)\) None 0 4
2925.1.cm \(\chi_{2925}(332, \cdot)\) None 0 4
2925.1.cp \(\chi_{2925}(743, \cdot)\) None 0 4
2925.1.cr \(\chi_{2925}(907, \cdot)\) None 0 4
2925.1.cs \(\chi_{2925}(349, \cdot)\) None 0 4
2925.1.ct \(\chi_{2925}(526, \cdot)\) None 0 4
2925.1.cx \(\chi_{2925}(607, \cdot)\) None 0 4
2925.1.cy \(\chi_{2925}(568, \cdot)\) 2925.1.cy.a 8 4
2925.1.cy.b 8
2925.1.db \(\chi_{2925}(157, \cdot)\) None 0 4
2925.1.dc \(\chi_{2925}(1582, \cdot)\) None 0 4
2925.1.dg \(\chi_{2925}(151, \cdot)\) 2925.1.dg.a 4 4
2925.1.dg.b 4
2925.1.dh \(\chi_{2925}(124, \cdot)\) None 0 4
2925.1.di \(\chi_{2925}(76, \cdot)\) None 0 4
2925.1.dj \(\chi_{2925}(499, \cdot)\) 2925.1.dj.a 4 4
2925.1.dj.b 4
2925.1.do \(\chi_{2925}(1099, \cdot)\) 2925.1.do.a 4 4
2925.1.do.b 4
2925.1.dp \(\chi_{2925}(1801, \cdot)\) 2925.1.dp.a 4 4
2925.1.dp.b 4
2925.1.dq \(\chi_{2925}(82, \cdot)\) 2925.1.dq.a 8 4
2925.1.dt \(\chi_{2925}(43, \cdot)\) None 0 4
2925.1.du \(\chi_{2925}(493, \cdot)\) None 0 4
2925.1.dw \(\chi_{2925}(518, \cdot)\) None 0 4
2925.1.dz \(\chi_{2925}(707, \cdot)\) None 0 4
2925.1.ea \(\chi_{2925}(782, \cdot)\) None 0 4
2925.1.ec \(\chi_{2925}(968, \cdot)\) None 0 4
2925.1.ej \(\chi_{2925}(242, \cdot)\) None 0 8
2925.1.el \(\chi_{2925}(352, \cdot)\) None 0 8
2925.1.em \(\chi_{2925}(109, \cdot)\) None 0 8
2925.1.en \(\chi_{2925}(541, \cdot)\) None 0 8
2925.1.er \(\chi_{2925}(298, \cdot)\) 2925.1.er.a 32 8
2925.1.es \(\chi_{2925}(8, \cdot)\) None 0 8
2925.1.ev \(\chi_{2925}(446, \cdot)\) None 0 8
2925.1.ew \(\chi_{2925}(29, \cdot)\) None 0 8
2925.1.ez \(\chi_{2925}(131, \cdot)\) None 0 8
2925.1.fa \(\chi_{2925}(341, \cdot)\) None 0 8
2925.1.fb \(\chi_{2925}(194, \cdot)\) None 0 8
2925.1.fc \(\chi_{2925}(134, \cdot)\) None 0 8
2925.1.fh \(\chi_{2925}(191, \cdot)\) None 0 8
2925.1.fi \(\chi_{2925}(959, \cdot)\) None 0 8
2925.1.fj \(\chi_{2925}(419, \cdot)\) None 0 8
2925.1.fk \(\chi_{2925}(56, \cdot)\) None 0 8
2925.1.fn \(\chi_{2925}(14, \cdot)\) None 0 8
2925.1.fo \(\chi_{2925}(269, \cdot)\) None 0 8
2925.1.fp \(\chi_{2925}(311, \cdot)\) None 0 8
2925.1.fq \(\chi_{2925}(296, \cdot)\) None 0 8
2925.1.fs \(\chi_{2925}(329, \cdot)\) None 0 8
2925.1.ft \(\chi_{2925}(146, \cdot)\) None 0 8
2925.1.fw \(\chi_{2925}(353, \cdot)\) None 0 16
2925.1.fy \(\chi_{2925}(227, \cdot)\) None 0 16
2925.1.gb \(\chi_{2925}(98, \cdot)\) None 0 16
2925.1.gc \(\chi_{2925}(122, \cdot)\) None 0 16
2925.1.gf \(\chi_{2925}(103, \cdot)\) None 0 16
2925.1.gg \(\chi_{2925}(277, \cdot)\) None 0 16
2925.1.gj \(\chi_{2925}(127, \cdot)\) None 0 16
2925.1.gk \(\chi_{2925}(46, \cdot)\) None 0 16
2925.1.gl \(\chi_{2925}(19, \cdot)\) None 0 16
2925.1.gq \(\chi_{2925}(34, \cdot)\) None 0 16
2925.1.gr \(\chi_{2925}(241, \cdot)\) None 0 16
2925.1.gs \(\chi_{2925}(184, \cdot)\) None 0 16
2925.1.gt \(\chi_{2925}(31, \cdot)\) None 0 16
2925.1.gx \(\chi_{2925}(178, \cdot)\) None 0 16
2925.1.gy \(\chi_{2925}(313, \cdot)\) None 0 16
2925.1.hb \(\chi_{2925}(172, \cdot)\) None 0 16
2925.1.hc \(\chi_{2925}(22, \cdot)\) None 0 16
2925.1.hg \(\chi_{2925}(106, \cdot)\) None 0 16
2925.1.hh \(\chi_{2925}(319, \cdot)\) None 0 16
2925.1.hi \(\chi_{2925}(88, \cdot)\) None 0 16
2925.1.hl \(\chi_{2925}(188, \cdot)\) None 0 16
2925.1.hm \(\chi_{2925}(47, \cdot)\) None 0 16
2925.1.hp \(\chi_{2925}(137, \cdot)\) None 0 16
2925.1.hr \(\chi_{2925}(2, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2925))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2925)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 2}\)