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Properties

Label 2013.1
Level 2013
Weight 1
Dimension 32
Nonzero newspaces 1
Newform subspaces 4
Sturm bound 297600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 4 \)
Sturm bound: \(297600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2013))\).

Total New Old
Modular forms 2490 1096 1394
Cusp forms 90 32 58
Eisenstein series 2400 1064 1336

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

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

Trace form

\( 32 q - 8 q^{4} - 8 q^{9} + O(q^{10}) \) \( 32 q - 8 q^{4} - 8 q^{9} - 8 q^{16} - 8 q^{25} - 8 q^{36} - 16 q^{46} - 16 q^{48} - 8 q^{49} - 16 q^{52} + 24 q^{58} - 8 q^{64} - 8 q^{66} + 64 q^{76} - 8 q^{81} - 8 q^{88} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2013))\)

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
2013.1.c \(\chi_{2013}(1343, \cdot)\) None 0 1
2013.1.d \(\chi_{2013}(1099, \cdot)\) None 0 1
2013.1.g \(\chi_{2013}(914, \cdot)\) None 0 1
2013.1.h \(\chi_{2013}(670, \cdot)\) None 0 1
2013.1.k \(\chi_{2013}(133, \cdot)\) None 0 2
2013.1.l \(\chi_{2013}(560, \cdot)\) None 0 2
2013.1.t \(\chi_{2013}(109, \cdot)\) None 0 2
2013.1.u \(\chi_{2013}(353, \cdot)\) None 0 2
2013.1.x \(\chi_{2013}(901, \cdot)\) None 0 2
2013.1.y \(\chi_{2013}(1145, \cdot)\) None 0 2
2013.1.bb \(\chi_{2013}(424, \cdot)\) None 0 4
2013.1.bc \(\chi_{2013}(20, \cdot)\) None 0 4
2013.1.be \(\chi_{2013}(125, \cdot)\) None 0 4
2013.1.bg \(\chi_{2013}(637, \cdot)\) None 0 4
2013.1.bh \(\chi_{2013}(601, \cdot)\) None 0 4
2013.1.bi \(\chi_{2013}(304, \cdot)\) None 0 4
2013.1.bj \(\chi_{2013}(613, \cdot)\) None 0 4
2013.1.bk \(\chi_{2013}(224, \cdot)\) None 0 4
2013.1.bm \(\chi_{2013}(548, \cdot)\) 2013.1.bm.a 4 4
2013.1.bm.b 4
2013.1.bm.c 8
2013.1.bm.d 16
2013.1.bp \(\chi_{2013}(1406, \cdot)\) None 0 4
2013.1.br \(\chi_{2013}(881, \cdot)\) None 0 4
2013.1.bs \(\chi_{2013}(712, \cdot)\) None 0 4
2013.1.bt \(\chi_{2013}(851, \cdot)\) None 0 4
2013.1.bw \(\chi_{2013}(1168, \cdot)\) None 0 4
2013.1.by \(\chi_{2013}(184, \cdot)\) None 0 4
2013.1.bz \(\chi_{2013}(142, \cdot)\) None 0 4
2013.1.cb \(\chi_{2013}(217, \cdot)\) None 0 4
2013.1.ce \(\chi_{2013}(119, \cdot)\) None 0 4
2013.1.cg \(\chi_{2013}(386, \cdot)\) None 0 4
2013.1.ch \(\chi_{2013}(245, \cdot)\) None 0 4
2013.1.cj \(\chi_{2013}(680, \cdot)\) None 0 4
2013.1.cm \(\chi_{2013}(985, \cdot)\) None 0 4
2013.1.cn \(\chi_{2013}(52, \cdot)\) None 0 4
2013.1.co \(\chi_{2013}(113, \cdot)\) None 0 4
2013.1.cr \(\chi_{2013}(32, \cdot)\) None 0 4
2013.1.cs \(\chi_{2013}(265, \cdot)\) None 0 4
2013.1.db \(\chi_{2013}(206, \cdot)\) None 0 8
2013.1.dc \(\chi_{2013}(577, \cdot)\) None 0 8
2013.1.de \(\chi_{2013}(130, \cdot)\) None 0 8
2013.1.dg \(\chi_{2013}(98, \cdot)\) None 0 8
2013.1.dk \(\chi_{2013}(8, \cdot)\) None 0 8
2013.1.dl \(\chi_{2013}(50, \cdot)\) None 0 8
2013.1.dm \(\chi_{2013}(272, \cdot)\) None 0 8
2013.1.dp \(\chi_{2013}(37, \cdot)\) None 0 8
2013.1.dq \(\chi_{2013}(355, \cdot)\) None 0 8
2013.1.dr \(\chi_{2013}(394, \cdot)\) None 0 8
2013.1.dv \(\chi_{2013}(496, \cdot)\) None 0 8
2013.1.dx \(\chi_{2013}(821, \cdot)\) None 0 8
2013.1.dz \(\chi_{2013}(290, \cdot)\) None 0 8
2013.1.ea \(\chi_{2013}(838, \cdot)\) None 0 8
2013.1.eb \(\chi_{2013}(205, \cdot)\) None 0 8
2013.1.ee \(\chi_{2013}(137, \cdot)\) None 0 8
2013.1.eg \(\chi_{2013}(47, \cdot)\) None 0 8
2013.1.eh \(\chi_{2013}(56, \cdot)\) None 0 8
2013.1.ej \(\chi_{2013}(269, \cdot)\) None 0 8
2013.1.em \(\chi_{2013}(391, \cdot)\) None 0 8
2013.1.eo \(\chi_{2013}(76, \cdot)\) None 0 8
2013.1.ep \(\chi_{2013}(13, \cdot)\) None 0 8
2013.1.er \(\chi_{2013}(178, \cdot)\) None 0 8
2013.1.eu \(\chi_{2013}(317, \cdot)\) None 0 8
2013.1.ev \(\chi_{2013}(46, \cdot)\) None 0 8
2013.1.ew \(\chi_{2013}(188, \cdot)\) None 0 8
2013.1.ey \(\chi_{2013}(476, \cdot)\) None 0 8
2013.1.fb \(\chi_{2013}(14, \cdot)\) None 0 8
2013.1.fd \(\chi_{2013}(80, \cdot)\) None 0 8
2013.1.fe \(\chi_{2013}(19, \cdot)\) None 0 8
2013.1.ff \(\chi_{2013}(292, \cdot)\) None 0 8
2013.1.fg \(\chi_{2013}(370, \cdot)\) None 0 8
2013.1.fh \(\chi_{2013}(472, \cdot)\) None 0 8
2013.1.fj \(\chi_{2013}(5, \cdot)\) None 0 8
2013.1.fl \(\chi_{2013}(86, \cdot)\) None 0 8
2013.1.fm \(\chi_{2013}(73, \cdot)\) None 0 8
2013.1.fo \(\chi_{2013}(17, \cdot)\) None 0 16
2013.1.fq \(\chi_{2013}(67, \cdot)\) None 0 16
2013.1.fu \(\chi_{2013}(82, \cdot)\) None 0 16
2013.1.fv \(\chi_{2013}(115, \cdot)\) None 0 16
2013.1.fw \(\chi_{2013}(124, \cdot)\) None 0 16
2013.1.fz \(\chi_{2013}(200, \cdot)\) None 0 16
2013.1.ga \(\chi_{2013}(2, \cdot)\) None 0 16
2013.1.gb \(\chi_{2013}(29, \cdot)\) None 0 16
2013.1.gf \(\chi_{2013}(494, \cdot)\) None 0 16
2013.1.gh \(\chi_{2013}(91, \cdot)\) None 0 16
2013.1.gj \(\chi_{2013}(31, \cdot)\) None 0 16
2013.1.gk \(\chi_{2013}(68, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2013))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2013)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(671))\)\(^{\oplus 2}\)