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Properties

Label 5800.2
Level 5800
Weight 2
Dimension 519127
Nonzero newspaces 64
Sturm bound 4032000

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Defining parameters

Level: \( N \) = \( 5800 = 2^{3} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(4032000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5800))\).

Total New Old
Modular forms 1017408 523555 493853
Cusp forms 998593 519127 479466
Eisenstein series 18815 4428 14387

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5800))\)

We only show spaces with even 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
5800.2.a \(\chi_{5800}(1, \cdot)\) 5800.2.a.a 1 1
5800.2.a.b 1
5800.2.a.c 1
5800.2.a.d 1
5800.2.a.e 1
5800.2.a.f 1
5800.2.a.g 1
5800.2.a.h 1
5800.2.a.i 1
5800.2.a.j 1
5800.2.a.k 1
5800.2.a.l 1
5800.2.a.m 1
5800.2.a.n 1
5800.2.a.o 2
5800.2.a.p 3
5800.2.a.q 3
5800.2.a.r 3
5800.2.a.s 3
5800.2.a.t 5
5800.2.a.u 5
5800.2.a.v 5
5800.2.a.w 6
5800.2.a.x 6
5800.2.a.y 6
5800.2.a.z 6
5800.2.a.ba 7
5800.2.a.bb 7
5800.2.a.bc 7
5800.2.a.bd 7
5800.2.a.be 8
5800.2.a.bf 8
5800.2.a.bg 11
5800.2.a.bh 11
5800.2.d \(\chi_{5800}(3249, \cdot)\) n/a 126 1
5800.2.e \(\chi_{5800}(4349, \cdot)\) n/a 536 1
5800.2.f \(\chi_{5800}(2901, \cdot)\) n/a 532 1
5800.2.g \(\chi_{5800}(4001, \cdot)\) n/a 142 1
5800.2.j \(\chi_{5800}(1449, \cdot)\) n/a 136 1
5800.2.k \(\chi_{5800}(349, \cdot)\) n/a 504 1
5800.2.p \(\chi_{5800}(1101, \cdot)\) n/a 564 1
5800.2.q \(\chi_{5800}(157, \cdot)\) n/a 1072 2
5800.2.s \(\chi_{5800}(2593, \cdot)\) n/a 270 2
5800.2.u \(\chi_{5800}(1351, \cdot)\) None 0 2
5800.2.w \(\chi_{5800}(2651, \cdot)\) n/a 1128 2
5800.2.ba \(\chi_{5800}(407, \cdot)\) None 0 2
5800.2.bb \(\chi_{5800}(1043, \cdot)\) n/a 1072 2
5800.2.bc \(\chi_{5800}(2843, \cdot)\) n/a 1008 2
5800.2.bd \(\chi_{5800}(3943, \cdot)\) None 0 2
5800.2.bh \(\chi_{5800}(99, \cdot)\) n/a 1072 2
5800.2.bj \(\chi_{5800}(2999, \cdot)\) None 0 2
5800.2.bl \(\chi_{5800}(3057, \cdot)\) n/a 270 2
5800.2.bn \(\chi_{5800}(1757, \cdot)\) n/a 1072 2
5800.2.bo \(\chi_{5800}(1161, \cdot)\) n/a 840 4
5800.2.bp \(\chi_{5800}(401, \cdot)\) n/a 858 6
5800.2.bs \(\chi_{5800}(1509, \cdot)\) n/a 3360 4
5800.2.bt \(\chi_{5800}(289, \cdot)\) n/a 896 4
5800.2.bu \(\chi_{5800}(2261, \cdot)\) n/a 3584 4
5800.2.bx \(\chi_{5800}(869, \cdot)\) n/a 3584 4
5800.2.by \(\chi_{5800}(929, \cdot)\) n/a 840 4
5800.2.cd \(\chi_{5800}(521, \cdot)\) n/a 904 4
5800.2.ce \(\chi_{5800}(581, \cdot)\) n/a 3360 4
5800.2.cf \(\chi_{5800}(701, \cdot)\) n/a 3384 6
5800.2.ck \(\chi_{5800}(749, \cdot)\) n/a 3216 6
5800.2.cl \(\chi_{5800}(1049, \cdot)\) n/a 816 6
5800.2.co \(\chi_{5800}(1401, \cdot)\) n/a 852 6
5800.2.cp \(\chi_{5800}(1301, \cdot)\) n/a 3384 6
5800.2.cq \(\chi_{5800}(149, \cdot)\) n/a 3216 6
5800.2.cr \(\chi_{5800}(49, \cdot)\) n/a 804 6
5800.2.cu \(\chi_{5800}(597, \cdot)\) n/a 7168 8
5800.2.cw \(\chi_{5800}(713, \cdot)\) n/a 1800 8
5800.2.cz \(\chi_{5800}(331, \cdot)\) n/a 7168 8
5800.2.db \(\chi_{5800}(191, \cdot)\) None 0 8
5800.2.de \(\chi_{5800}(463, \cdot)\) None 0 8
5800.2.df \(\chi_{5800}(523, \cdot)\) n/a 6720 8
5800.2.dg \(\chi_{5800}(347, \cdot)\) n/a 7168 8
5800.2.dh \(\chi_{5800}(1103, \cdot)\) None 0 8
5800.2.dk \(\chi_{5800}(679, \cdot)\) None 0 8
5800.2.dm \(\chi_{5800}(539, \cdot)\) n/a 7168 8
5800.2.dp \(\chi_{5800}(17, \cdot)\) n/a 1800 8
5800.2.dr \(\chi_{5800}(133, \cdot)\) n/a 7168 8
5800.2.ds \(\chi_{5800}(193, \cdot)\) n/a 1620 12
5800.2.du \(\chi_{5800}(693, \cdot)\) n/a 6432 12
5800.2.dw \(\chi_{5800}(599, \cdot)\) None 0 12
5800.2.dy \(\chi_{5800}(699, \cdot)\) n/a 6432 12
5800.2.ec \(\chi_{5800}(207, \cdot)\) None 0 12
5800.2.ed \(\chi_{5800}(107, \cdot)\) n/a 6432 12
5800.2.ee \(\chi_{5800}(643, \cdot)\) n/a 6432 12
5800.2.ef \(\chi_{5800}(7, \cdot)\) None 0 12
5800.2.ej \(\chi_{5800}(251, \cdot)\) n/a 6768 12
5800.2.el \(\chi_{5800}(351, \cdot)\) None 0 12
5800.2.en \(\chi_{5800}(293, \cdot)\) n/a 6432 12
5800.2.ep \(\chi_{5800}(657, \cdot)\) n/a 1620 12
5800.2.eq \(\chi_{5800}(81, \cdot)\) n/a 5376 24
5800.2.er \(\chi_{5800}(141, \cdot)\) n/a 21504 24
5800.2.es \(\chi_{5800}(121, \cdot)\) n/a 5424 24
5800.2.ex \(\chi_{5800}(169, \cdot)\) n/a 5424 24
5800.2.ey \(\chi_{5800}(109, \cdot)\) n/a 21504 24
5800.2.fb \(\chi_{5800}(341, \cdot)\) n/a 21504 24
5800.2.fc \(\chi_{5800}(9, \cdot)\) n/a 5376 24
5800.2.fd \(\chi_{5800}(429, \cdot)\) n/a 21504 24
5800.2.fg \(\chi_{5800}(73, \cdot)\) n/a 10800 48
5800.2.fi \(\chi_{5800}(37, \cdot)\) n/a 43008 48
5800.2.fl \(\chi_{5800}(19, \cdot)\) n/a 43008 48
5800.2.fn \(\chi_{5800}(39, \cdot)\) None 0 48
5800.2.fq \(\chi_{5800}(23, \cdot)\) None 0 48
5800.2.fr \(\chi_{5800}(67, \cdot)\) n/a 43008 48
5800.2.fs \(\chi_{5800}(83, \cdot)\) n/a 43008 48
5800.2.ft \(\chi_{5800}(63, \cdot)\) None 0 48
5800.2.fw \(\chi_{5800}(31, \cdot)\) None 0 48
5800.2.fy \(\chi_{5800}(11, \cdot)\) n/a 43008 48
5800.2.gb \(\chi_{5800}(77, \cdot)\) n/a 43008 48
5800.2.gd \(\chi_{5800}(97, \cdot)\) n/a 10800 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2900))\)\(^{\oplus 2}\)