# Properties

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

## 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

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