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Properties

Label 5950.2
Level 5950
Weight 2
Dimension 303140
Nonzero newspaces 72
Sturm bound 4147200

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Defining parameters

Level: \( N \) = \( 5950 = 2 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(4147200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5950))\).

Total New Old
Modular forms 1047552 303140 744412
Cusp forms 1026049 303140 722909
Eisenstein series 21503 0 21503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5950))\)

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
5950.2.a \(\chi_{5950}(1, \cdot)\) 5950.2.a.a 1 1
5950.2.a.b 1
5950.2.a.c 1
5950.2.a.d 1
5950.2.a.e 1
5950.2.a.f 1
5950.2.a.g 1
5950.2.a.h 1
5950.2.a.i 1
5950.2.a.j 1
5950.2.a.k 1
5950.2.a.l 1
5950.2.a.m 1
5950.2.a.n 1
5950.2.a.o 1
5950.2.a.p 1
5950.2.a.q 1
5950.2.a.r 1
5950.2.a.s 1
5950.2.a.t 2
5950.2.a.u 2
5950.2.a.v 2
5950.2.a.w 2
5950.2.a.x 2
5950.2.a.y 2
5950.2.a.z 2
5950.2.a.ba 2
5950.2.a.bb 3
5950.2.a.bc 3
5950.2.a.bd 3
5950.2.a.be 3
5950.2.a.bf 3
5950.2.a.bg 3
5950.2.a.bh 3
5950.2.a.bi 3
5950.2.a.bj 3
5950.2.a.bk 3
5950.2.a.bl 3
5950.2.a.bm 3
5950.2.a.bn 4
5950.2.a.bo 4
5950.2.a.bp 4
5950.2.a.bq 4
5950.2.a.br 4
5950.2.a.bs 5
5950.2.a.bt 5
5950.2.a.bu 5
5950.2.a.bv 5
5950.2.a.bw 5
5950.2.a.bx 5
5950.2.a.by 5
5950.2.a.bz 6
5950.2.a.ca 6
5950.2.a.cb 7
5950.2.a.cc 7
5950.2.c \(\chi_{5950}(3501, \cdot)\) n/a 172 1
5950.2.e \(\chi_{5950}(4999, \cdot)\) n/a 144 1
5950.2.g \(\chi_{5950}(2549, \cdot)\) n/a 160 1
5950.2.i \(\chi_{5950}(851, \cdot)\) n/a 408 2
5950.2.j \(\chi_{5950}(293, \cdot)\) n/a 432 2
5950.2.m \(\chi_{5950}(3093, \cdot)\) n/a 432 2
5950.2.n \(\chi_{5950}(1849, \cdot)\) n/a 320 2
5950.2.p \(\chi_{5950}(701, \cdot)\) n/a 344 2
5950.2.s \(\chi_{5950}(307, \cdot)\) n/a 384 2
5950.2.t \(\chi_{5950}(1007, \cdot)\) n/a 432 2
5950.2.v \(\chi_{5950}(1191, \cdot)\) n/a 960 4
5950.2.x \(\chi_{5950}(849, \cdot)\) n/a 432 2
5950.2.z \(\chi_{5950}(3299, \cdot)\) n/a 384 2
5950.2.bb \(\chi_{5950}(1801, \cdot)\) n/a 456 2
5950.2.be \(\chi_{5950}(3851, \cdot)\) n/a 680 4
5950.2.bg \(\chi_{5950}(3443, \cdot)\) n/a 864 4
5950.2.bi \(\chi_{5950}(3793, \cdot)\) n/a 864 4
5950.2.bj \(\chi_{5950}(2899, \cdot)\) n/a 656 4
5950.2.bm \(\chi_{5950}(169, \cdot)\) n/a 1088 4
5950.2.bo \(\chi_{5950}(239, \cdot)\) n/a 960 4
5950.2.bq \(\chi_{5950}(1121, \cdot)\) n/a 1072 4
5950.2.bt \(\chi_{5950}(157, \cdot)\) n/a 864 4
5950.2.bu \(\chi_{5950}(1293, \cdot)\) n/a 768 4
5950.2.bx \(\chi_{5950}(149, \cdot)\) n/a 864 4
5950.2.bz \(\chi_{5950}(1101, \cdot)\) n/a 912 4
5950.2.ca \(\chi_{5950}(2243, \cdot)\) n/a 864 4
5950.2.cd \(\chi_{5950}(1993, \cdot)\) n/a 864 4
5950.2.ce \(\chi_{5950}(681, \cdot)\) n/a 2560 8
5950.2.cf \(\chi_{5950}(57, \cdot)\) n/a 1296 8
5950.2.ci \(\chi_{5950}(1049, \cdot)\) n/a 1728 8
5950.2.cj \(\chi_{5950}(601, \cdot)\) n/a 1824 8
5950.2.cl \(\chi_{5950}(1457, \cdot)\) n/a 1296 8
5950.2.co \(\chi_{5950}(13, \cdot)\) n/a 2880 8
5950.2.cp \(\chi_{5950}(783, \cdot)\) n/a 2560 8
5950.2.cs \(\chi_{5950}(421, \cdot)\) n/a 2144 8
5950.2.cu \(\chi_{5950}(659, \cdot)\) n/a 2176 8
5950.2.cv \(\chi_{5950}(237, \cdot)\) n/a 2880 8
5950.2.cy \(\chi_{5950}(727, \cdot)\) n/a 2880 8
5950.2.cz \(\chi_{5950}(151, \cdot)\) n/a 1824 8
5950.2.dc \(\chi_{5950}(257, \cdot)\) n/a 1728 8
5950.2.de \(\chi_{5950}(593, \cdot)\) n/a 1728 8
5950.2.dg \(\chi_{5950}(1199, \cdot)\) n/a 1728 8
5950.2.di \(\chi_{5950}(611, \cdot)\) n/a 2880 8
5950.2.dk \(\chi_{5950}(919, \cdot)\) n/a 2560 8
5950.2.dm \(\chi_{5950}(1019, \cdot)\) n/a 2880 8
5950.2.dp \(\chi_{5950}(519, \cdot)\) n/a 4288 16
5950.2.dq \(\chi_{5950}(433, \cdot)\) n/a 5760 16
5950.2.ds \(\chi_{5950}(83, \cdot)\) n/a 5760 16
5950.2.du \(\chi_{5950}(281, \cdot)\) n/a 4352 16
5950.2.dw \(\chi_{5950}(907, \cdot)\) n/a 3456 16
5950.2.dz \(\chi_{5950}(201, \cdot)\) n/a 3648 16
5950.2.ea \(\chi_{5950}(199, \cdot)\) n/a 3456 16
5950.2.ec \(\chi_{5950}(107, \cdot)\) n/a 3456 16
5950.2.ee \(\chi_{5950}(47, \cdot)\) n/a 5760 16
5950.2.eh \(\chi_{5950}(33, \cdot)\) n/a 5760 16
5950.2.ei \(\chi_{5950}(81, \cdot)\) n/a 5760 16
5950.2.ek \(\chi_{5950}(319, \cdot)\) n/a 5760 16
5950.2.en \(\chi_{5950}(103, \cdot)\) n/a 5120 16
5950.2.eo \(\chi_{5950}(327, \cdot)\) n/a 5760 16
5950.2.er \(\chi_{5950}(113, \cdot)\) n/a 8640 32
5950.2.et \(\chi_{5950}(41, \cdot)\) n/a 11520 32
5950.2.eu \(\chi_{5950}(139, \cdot)\) n/a 11520 32
5950.2.ex \(\chi_{5950}(197, \cdot)\) n/a 8640 32
5950.2.ey \(\chi_{5950}(9, \cdot)\) n/a 11520 32
5950.2.fa \(\chi_{5950}(87, \cdot)\) n/a 11520 32
5950.2.fc \(\chi_{5950}(297, \cdot)\) n/a 11520 32
5950.2.ff \(\chi_{5950}(121, \cdot)\) n/a 11520 32
5950.2.fh \(\chi_{5950}(23, \cdot)\) n/a 23040 64
5950.2.fj \(\chi_{5950}(129, \cdot)\) n/a 23040 64
5950.2.fk \(\chi_{5950}(31, \cdot)\) n/a 23040 64
5950.2.fn \(\chi_{5950}(177, \cdot)\) n/a 23040 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2975))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5950))\)\(^{\oplus 1}\)