Properties

Label 2583.1
Level 2583
Weight 1
Dimension 34
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 483840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2583\( 2583 = 3^{2} \cdot 7 \cdot 41 \) \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(483840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2583))\).

Total New Old
Modular forms 3894 1788 2106
Cusp forms 54 34 20
Eisenstein series 3840 1754 2086

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 34 0 0 0

Trace form

\( 34q + 2q^{2} - 10q^{4} + 4q^{8} + O(q^{10}) \) \( 34q + 2q^{2} - 10q^{4} + 4q^{8} - 12q^{16} + 2q^{23} - 8q^{25} + 6q^{32} - 2q^{37} - 2q^{43} - 4q^{46} - 8q^{49} + 2q^{50} + 28q^{64} + 28q^{72} + 4q^{74} - 14q^{78} - 14q^{84} + 4q^{86} - 2q^{91} - 36q^{92} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2583))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2583.1.b \(\chi_{2583}(575, \cdot)\) None 0 1
2583.1.c \(\chi_{2583}(2213, \cdot)\) None 0 1
2583.1.f \(\chi_{2583}(2008, \cdot)\) 2583.1.f.a 3 1
2583.1.f.b 3
2583.1.g \(\chi_{2583}(370, \cdot)\) None 0 1
2583.1.n \(\chi_{2583}(811, \cdot)\) None 0 2
2583.1.p \(\chi_{2583}(1016, \cdot)\) None 0 2
2583.1.t \(\chi_{2583}(1598, \cdot)\) None 0 2
2583.1.u \(\chi_{2583}(452, \cdot)\) None 0 2
2583.1.v \(\chi_{2583}(409, \cdot)\) None 0 2
2583.1.w \(\chi_{2583}(124, \cdot)\) None 0 2
2583.1.z \(\chi_{2583}(1231, \cdot)\) None 0 2
2583.1.ba \(\chi_{2583}(286, \cdot)\) 2583.1.ba.a 2 2
2583.1.ba.b 2
2583.1.ba.c 12
2583.1.ba.d 12
2583.1.bb \(\chi_{2583}(1846, \cdot)\) None 0 2
2583.1.bc \(\chi_{2583}(901, \cdot)\) None 0 2
2583.1.be \(\chi_{2583}(821, \cdot)\) None 0 2
2583.1.bf \(\chi_{2583}(1229, \cdot)\) None 0 2
2583.1.bk \(\chi_{2583}(368, \cdot)\) None 0 2
2583.1.bl \(\chi_{2583}(1313, \cdot)\) None 0 2
2583.1.bm \(\chi_{2583}(491, \cdot)\) None 0 2
2583.1.bn \(\chi_{2583}(1436, \cdot)\) None 0 2
2583.1.br \(\chi_{2583}(493, \cdot)\) None 0 2
2583.1.bs \(\chi_{2583}(40, \cdot)\) None 0 2
2583.1.bu \(\chi_{2583}(314, \cdot)\) None 0 4
2583.1.bv \(\chi_{2583}(694, \cdot)\) None 0 4
2583.1.by \(\chi_{2583}(748, \cdot)\) None 0 4
2583.1.bz \(\chi_{2583}(433, \cdot)\) None 0 4
2583.1.cc \(\chi_{2583}(638, \cdot)\) None 0 4
2583.1.cd \(\chi_{2583}(953, \cdot)\) None 0 4
2583.1.ce \(\chi_{2583}(934, \cdot)\) None 0 4
2583.1.ch \(\chi_{2583}(296, \cdot)\) None 0 4
2583.1.ci \(\chi_{2583}(50, \cdot)\) None 0 4
2583.1.cl \(\chi_{2583}(32, \cdot)\) None 0 4
2583.1.cn \(\chi_{2583}(706, \cdot)\) None 0 4
2583.1.co \(\chi_{2583}(73, \cdot)\) None 0 4
2583.1.cr \(\chi_{2583}(565, \cdot)\) None 0 4
2583.1.cs \(\chi_{2583}(401, \cdot)\) None 0 4
2583.1.cy \(\chi_{2583}(8, \cdot)\) None 0 8
2583.1.da \(\chi_{2583}(118, \cdot)\) None 0 8
2583.1.dd \(\chi_{2583}(940, \cdot)\) None 0 8
2583.1.de \(\chi_{2583}(38, \cdot)\) None 0 8
2583.1.dg \(\chi_{2583}(167, \cdot)\) None 0 8
2583.1.di \(\chi_{2583}(79, \cdot)\) None 0 8
2583.1.dk \(\chi_{2583}(109, \cdot)\) None 0 8
2583.1.dn \(\chi_{2583}(530, \cdot)\) None 0 8
2583.1.dp \(\chi_{2583}(437, \cdot)\) None 0 8
2583.1.dr \(\chi_{2583}(85, \cdot)\) None 0 8
2583.1.ds \(\chi_{2583}(556, \cdot)\) None 0 8
2583.1.dt \(\chi_{2583}(871, \cdot)\) None 0 8
2583.1.dx \(\chi_{2583}(92, \cdot)\) None 0 8
2583.1.dy \(\chi_{2583}(113, \cdot)\) None 0 8
2583.1.dz \(\chi_{2583}(242, \cdot)\) None 0 8
2583.1.ea \(\chi_{2583}(107, \cdot)\) None 0 8
2583.1.ef \(\chi_{2583}(599, \cdot)\) None 0 8
2583.1.eg \(\chi_{2583}(221, \cdot)\) None 0 8
2583.1.ei \(\chi_{2583}(271, \cdot)\) None 0 8
2583.1.ej \(\chi_{2583}(10, \cdot)\) None 0 8
2583.1.ek \(\chi_{2583}(517, \cdot)\) None 0 8
2583.1.el \(\chi_{2583}(139, \cdot)\) None 0 8
2583.1.eo \(\chi_{2583}(283, \cdot)\) None 0 8
2583.1.ep \(\chi_{2583}(31, \cdot)\) None 0 8
2583.1.eq \(\chi_{2583}(338, \cdot)\) None 0 8
2583.1.er \(\chi_{2583}(23, \cdot)\) None 0 8
2583.1.ev \(\chi_{2583}(190, \cdot)\) None 0 16
2583.1.ew \(\chi_{2583}(188, \cdot)\) None 0 16
2583.1.ez \(\chi_{2583}(74, \cdot)\) None 0 16
2583.1.fa \(\chi_{2583}(61, \cdot)\) None 0 16
2583.1.fd \(\chi_{2583}(964, \cdot)\) None 0 16
2583.1.fe \(\chi_{2583}(349, \cdot)\) None 0 16
2583.1.fg \(\chi_{2583}(2, \cdot)\) None 0 16
2583.1.fj \(\chi_{2583}(554, \cdot)\) None 0 16
2583.1.fk \(\chi_{2583}(431, \cdot)\) None 0 16
2583.1.fn \(\chi_{2583}(103, \cdot)\) None 0 16
2583.1.fo \(\chi_{2583}(22, \cdot)\) None 0 32
2583.1.fq \(\chi_{2583}(47, \cdot)\) None 0 32
2583.1.fs \(\chi_{2583}(17, \cdot)\) None 0 32
2583.1.fv \(\chi_{2583}(235, \cdot)\) None 0 32
2583.1.fx \(\chi_{2583}(67, \cdot)\) None 0 32
2583.1.fz \(\chi_{2583}(104, \cdot)\) None 0 32
2583.1.gb \(\chi_{2583}(101, \cdot)\) None 0 32
2583.1.gc \(\chi_{2583}(58, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2583))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2583)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 3}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))
$3$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))
$5$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$7$ (\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6} \))
$11$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$13$ (\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2} \))
$17$ (\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2} \))
$19$ (\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{4} \))
$23$ (\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))
$29$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$31$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$37$ (\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))
$41$ (\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6} \))
$43$ (\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))
$47$ (\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2} \))
$53$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{12}( 1 + T )^{12} \))(\( ( 1 - T )^{12}( 1 + T )^{12} \))
$59$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$61$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$67$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$71$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{12}( 1 + T )^{12} \))(\( ( 1 - T )^{12}( 1 + T )^{12} \))
$73$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{12}( 1 + T )^{12} \))(\( ( 1 - T )^{12}( 1 + T )^{12} \))
$79$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$83$ (\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T )^{3}( 1 + T )^{3} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6}( 1 + T + T^{2} )^{6} \))
$89$ (\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2} \))
$97$ (\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} ) \))
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