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Properties

Label 5239.2
Level 5239
Weight 2
Dimension 1114013
Nonzero newspaces 60
Sturm bound 4542720

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Defining parameters

Level: \( N \) = \( 5239 = 13^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(4542720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5239))\).

Total New Old
Modular forms 1142520 1125873 16647
Cusp forms 1128841 1114013 14828
Eisenstein series 13679 11860 1819

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5239))\)

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
5239.2.a \(\chi_{5239}(1, \cdot)\) 5239.2.a.a 1 1
5239.2.a.b 1
5239.2.a.c 1
5239.2.a.d 1
5239.2.a.e 2
5239.2.a.f 2
5239.2.a.g 6
5239.2.a.h 7
5239.2.a.i 8
5239.2.a.j 8
5239.2.a.k 16
5239.2.a.l 16
5239.2.a.m 17
5239.2.a.n 17
5239.2.a.o 18
5239.2.a.p 18
5239.2.a.q 34
5239.2.a.r 34
5239.2.a.s 36
5239.2.a.t 36
5239.2.a.u 54
5239.2.a.v 54
5239.2.c \(\chi_{5239}(1520, \cdot)\) n/a 386 1
5239.2.e \(\chi_{5239}(191, \cdot)\) n/a 802 2
5239.2.f \(\chi_{5239}(2388, \cdot)\) n/a 768 2
5239.2.g \(\chi_{5239}(315, \cdot)\) n/a 802 2
5239.2.h \(\chi_{5239}(2536, \cdot)\) n/a 804 2
5239.2.i \(\chi_{5239}(1084, \cdot)\) n/a 804 2
5239.2.k \(\chi_{5239}(2705, \cdot)\) n/a 1612 4
5239.2.l \(\chi_{5239}(4055, \cdot)\) n/a 800 2
5239.2.r \(\chi_{5239}(4248, \cdot)\) n/a 772 2
5239.2.s \(\chi_{5239}(1544, \cdot)\) n/a 802 2
5239.2.v \(\chi_{5239}(1668, \cdot)\) n/a 802 2
5239.2.y \(\chi_{5239}(1182, \cdot)\) n/a 1608 4
5239.2.ba \(\chi_{5239}(657, \cdot)\) n/a 1604 4
5239.2.be \(\chi_{5239}(99, \cdot)\) n/a 1600 4
5239.2.bf \(\chi_{5239}(150, \cdot)\) n/a 1604 4
5239.2.bg \(\chi_{5239}(526, \cdot)\) n/a 1600 4
5239.2.bi \(\chi_{5239}(404, \cdot)\) n/a 5472 12
5239.2.bj \(\chi_{5239}(846, \cdot)\) n/a 3216 8
5239.2.bk \(\chi_{5239}(360, \cdot)\) n/a 3208 8
5239.2.bl \(\chi_{5239}(484, \cdot)\) n/a 3208 8
5239.2.bm \(\chi_{5239}(529, \cdot)\) n/a 3200 8
5239.2.bo \(\chi_{5239}(1422, \cdot)\) n/a 3216 8
5239.2.bq \(\chi_{5239}(311, \cdot)\) n/a 5448 12
5239.2.bt \(\chi_{5239}(361, \cdot)\) n/a 3208 8
5239.2.bw \(\chi_{5239}(1713, \cdot)\) n/a 3200 8
5239.2.bx \(\chi_{5239}(485, \cdot)\) n/a 3208 8
5239.2.cd \(\chi_{5239}(506, \cdot)\) n/a 3200 8
5239.2.ce \(\chi_{5239}(118, \cdot)\) n/a 11616 24
5239.2.cf \(\chi_{5239}(87, \cdot)\) n/a 11592 24
5239.2.cg \(\chi_{5239}(94, \cdot)\) n/a 10944 24
5239.2.ch \(\chi_{5239}(211, \cdot)\) n/a 11592 24
5239.2.cj \(\chi_{5239}(216, \cdot)\) n/a 11568 24
5239.2.cl \(\chi_{5239}(89, \cdot)\) n/a 6400 16
5239.2.cm \(\chi_{5239}(427, \cdot)\) n/a 6416 16
5239.2.cn \(\chi_{5239}(239, \cdot)\) n/a 6400 16
5239.2.cr \(\chi_{5239}(765, \cdot)\) n/a 6416 16
5239.2.cs \(\chi_{5239}(66, \cdot)\) n/a 23136 48
5239.2.cu \(\chi_{5239}(36, \cdot)\) n/a 11592 24
5239.2.cx \(\chi_{5239}(160, \cdot)\) n/a 11592 24
5239.2.cy \(\chi_{5239}(218, \cdot)\) n/a 10896 24
5239.2.de \(\chi_{5239}(25, \cdot)\) n/a 11616 24
5239.2.dg \(\chi_{5239}(64, \cdot)\) n/a 23136 48
5239.2.dj \(\chi_{5239}(123, \cdot)\) n/a 23232 48
5239.2.dk \(\chi_{5239}(37, \cdot)\) n/a 23184 48
5239.2.dl \(\chi_{5239}(57, \cdot)\) n/a 23232 48
5239.2.dp \(\chi_{5239}(6, \cdot)\) n/a 23184 48
5239.2.dq \(\chi_{5239}(16, \cdot)\) n/a 46464 96
5239.2.dr \(\chi_{5239}(9, \cdot)\) n/a 46368 96
5239.2.ds \(\chi_{5239}(100, \cdot)\) n/a 46368 96
5239.2.dt \(\chi_{5239}(14, \cdot)\) n/a 46464 96
5239.2.du \(\chi_{5239}(60, \cdot)\) n/a 46272 96
5239.2.dw \(\chi_{5239}(38, \cdot)\) n/a 46464 96
5239.2.ec \(\chi_{5239}(82, \cdot)\) n/a 46368 96
5239.2.ed \(\chi_{5239}(4, \cdot)\) n/a 46464 96
5239.2.eg \(\chi_{5239}(10, \cdot)\) n/a 46368 96
5239.2.ei \(\chi_{5239}(11, \cdot)\) n/a 92736 192
5239.2.em \(\chi_{5239}(21, \cdot)\) n/a 92928 192
5239.2.en \(\chi_{5239}(24, \cdot)\) n/a 92736 192
5239.2.eo \(\chi_{5239}(15, \cdot)\) n/a 92928 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5239))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5239)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 2}\)