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Properties

Label 2800.1
Level 2800
Weight 1
Dimension 108
Nonzero newspaces 11
Newform subspaces 28
Sturm bound 460800
Trace bound 49

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Defining parameters

Level: \( N \) = \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 28 \)
Sturm bound: \(460800\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2800))\).

Total New Old
Modular forms 5214 1031 4183
Cusp forms 510 108 402
Eisenstein series 4704 923 3781

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 76 0 32 0

Trace form

\( 108 q + 2 q^{4} + 16 q^{6} + 4 q^{9} + O(q^{10}) \) \( 108 q + 2 q^{4} + 16 q^{6} + 4 q^{9} + 16 q^{11} + 2 q^{14} - 18 q^{16} - 2 q^{18} + 12 q^{21} - 2 q^{22} - 8 q^{26} + 8 q^{29} + 2 q^{37} + 2 q^{39} + 4 q^{41} - 2 q^{43} - 2 q^{44} + 8 q^{46} - 2 q^{49} + 6 q^{51} - 2 q^{53} + 6 q^{56} + 2 q^{58} - 22 q^{61} - 2 q^{63} + 2 q^{64} - 2 q^{67} - 12 q^{69} + 2 q^{72} - 2 q^{74} + 32 q^{76} - 2 q^{77} - 2 q^{79} - 14 q^{81} - 6 q^{86} + 2 q^{88} - 2 q^{89} + 10 q^{91} - 8 q^{96} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2800))\)

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
2800.1.c \(\chi_{2800}(1049, \cdot)\) None 0 1
2800.1.d \(\chi_{2800}(351, \cdot)\) None 0 1
2800.1.f \(\chi_{2800}(2001, \cdot)\) 2800.1.f.a 1 1
2800.1.f.b 1
2800.1.f.c 2
2800.1.i \(\chi_{2800}(2199, \cdot)\) None 0 1
2800.1.j \(\chi_{2800}(799, \cdot)\) None 0 1
2800.1.m \(\chi_{2800}(601, \cdot)\) None 0 1
2800.1.o \(\chi_{2800}(1751, \cdot)\) None 0 1
2800.1.p \(\chi_{2800}(2449, \cdot)\) 2800.1.p.a 2 1
2800.1.s \(\chi_{2800}(757, \cdot)\) None 0 2
2800.1.u \(\chi_{2800}(643, \cdot)\) 2800.1.u.a 4 2
2800.1.u.b 8
2800.1.v \(\chi_{2800}(1007, \cdot)\) 2800.1.v.a 4 2
2800.1.v.b 8
2800.1.y \(\chi_{2800}(57, \cdot)\) None 0 2
2800.1.z \(\chi_{2800}(1301, \cdot)\) 2800.1.z.a 2 2
2800.1.z.b 4
2800.1.z.c 4
2800.1.ba \(\chi_{2800}(99, \cdot)\) None 0 2
2800.1.bf \(\chi_{2800}(349, \cdot)\) 2800.1.bf.a 2 2
2800.1.bf.b 2
2800.1.bf.c 4
2800.1.bf.d 4
2800.1.bg \(\chi_{2800}(1051, \cdot)\) None 0 2
2800.1.bh \(\chi_{2800}(1457, \cdot)\) None 0 2
2800.1.bk \(\chi_{2800}(2407, \cdot)\) None 0 2
2800.1.bm \(\chi_{2800}(307, \cdot)\) 2800.1.bm.a 4 2
2800.1.bm.b 8
2800.1.bo \(\chi_{2800}(1093, \cdot)\) None 0 2
2800.1.bq \(\chi_{2800}(151, \cdot)\) None 0 2
2800.1.bs \(\chi_{2800}(1249, \cdot)\) None 0 2
2800.1.bu \(\chi_{2800}(1199, \cdot)\) None 0 2
2800.1.bv \(\chi_{2800}(201, \cdot)\) None 0 2
2800.1.by \(\chi_{2800}(801, \cdot)\) None 0 2
2800.1.bz \(\chi_{2800}(599, \cdot)\) None 0 2
2800.1.cb \(\chi_{2800}(649, \cdot)\) None 0 2
2800.1.ce \(\chi_{2800}(751, \cdot)\) 2800.1.ce.a 2 2
2800.1.ce.b 2
2800.1.cf \(\chi_{2800}(209, \cdot)\) None 0 4
2800.1.cg \(\chi_{2800}(71, \cdot)\) None 0 4
2800.1.ci \(\chi_{2800}(41, \cdot)\) None 0 4
2800.1.cl \(\chi_{2800}(239, \cdot)\) None 0 4
2800.1.cm \(\chi_{2800}(519, \cdot)\) None 0 4
2800.1.cp \(\chi_{2800}(321, \cdot)\) None 0 4
2800.1.cr \(\chi_{2800}(911, \cdot)\) None 0 4
2800.1.cs \(\chi_{2800}(489, \cdot)\) None 0 4
2800.1.cu \(\chi_{2800}(843, \cdot)\) None 0 4
2800.1.cw \(\chi_{2800}(557, \cdot)\) None 0 4
2800.1.cz \(\chi_{2800}(1207, \cdot)\) None 0 4
2800.1.da \(\chi_{2800}(193, \cdot)\) None 0 4
2800.1.dc \(\chi_{2800}(51, \cdot)\) 2800.1.dc.a 4 4
2800.1.dc.b 4
2800.1.dc.c 4
2800.1.dc.d 4
2800.1.dd \(\chi_{2800}(549, \cdot)\) None 0 4
2800.1.di \(\chi_{2800}(499, \cdot)\) 2800.1.di.a 4 4
2800.1.di.b 4
2800.1.di.c 4
2800.1.di.d 4
2800.1.dj \(\chi_{2800}(101, \cdot)\) None 0 4
2800.1.dl \(\chi_{2800}(457, \cdot)\) None 0 4
2800.1.dm \(\chi_{2800}(143, \cdot)\) 2800.1.dm.a 8 4
2800.1.do \(\chi_{2800}(93, \cdot)\) None 0 4
2800.1.dq \(\chi_{2800}(243, \cdot)\) None 0 4
2800.1.dt \(\chi_{2800}(477, \cdot)\) None 0 8
2800.1.dv \(\chi_{2800}(363, \cdot)\) None 0 8
2800.1.dx \(\chi_{2800}(167, \cdot)\) None 0 8
2800.1.ea \(\chi_{2800}(113, \cdot)\) None 0 8
2800.1.eb \(\chi_{2800}(211, \cdot)\) None 0 8
2800.1.ec \(\chi_{2800}(69, \cdot)\) None 0 8
2800.1.eh \(\chi_{2800}(379, \cdot)\) None 0 8
2800.1.ei \(\chi_{2800}(181, \cdot)\) None 0 8
2800.1.ej \(\chi_{2800}(617, \cdot)\) None 0 8
2800.1.em \(\chi_{2800}(223, \cdot)\) None 0 8
2800.1.en \(\chi_{2800}(27, \cdot)\) None 0 8
2800.1.ep \(\chi_{2800}(197, \cdot)\) None 0 8
2800.1.er \(\chi_{2800}(191, \cdot)\) None 0 8
2800.1.eu \(\chi_{2800}(89, \cdot)\) None 0 8
2800.1.ew \(\chi_{2800}(39, \cdot)\) None 0 8
2800.1.ex \(\chi_{2800}(241, \cdot)\) None 0 8
2800.1.fa \(\chi_{2800}(521, \cdot)\) None 0 8
2800.1.fb \(\chi_{2800}(79, \cdot)\) None 0 8
2800.1.fd \(\chi_{2800}(129, \cdot)\) None 0 8
2800.1.ff \(\chi_{2800}(471, \cdot)\) None 0 8
2800.1.fh \(\chi_{2800}(3, \cdot)\) None 0 16
2800.1.fj \(\chi_{2800}(37, \cdot)\) None 0 16
2800.1.fl \(\chi_{2800}(47, \cdot)\) None 0 16
2800.1.fm \(\chi_{2800}(137, \cdot)\) None 0 16
2800.1.fo \(\chi_{2800}(61, \cdot)\) None 0 16
2800.1.fp \(\chi_{2800}(179, \cdot)\) None 0 16
2800.1.fu \(\chi_{2800}(229, \cdot)\) None 0 16
2800.1.fv \(\chi_{2800}(11, \cdot)\) None 0 16
2800.1.fx \(\chi_{2800}(177, \cdot)\) None 0 16
2800.1.fy \(\chi_{2800}(87, \cdot)\) None 0 16
2800.1.gb \(\chi_{2800}(53, \cdot)\) None 0 16
2800.1.gd \(\chi_{2800}(227, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2800))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2800)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1400))\)\(^{\oplus 2}\)