# Properties

 Label 2563.1.b Level 2563 Weight 1 Character orbit b Rep. character $$\chi_{2563}(2562,\cdot)$$ Character field $$\Q$$ Dimension 6 Newform subspaces 4 Sturm bound 234 Trace bound 11

# Related objects

## Defining parameters

 Level: $$N$$ = $$2563 = 11 \cdot 233$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 2563.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$2563$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$234$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2563, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 4 0

## Trace form

 $$6q - 2q^{4} - 2q^{9} + O(q^{10})$$ $$6q - 2q^{4} - 2q^{9} + 8q^{15} - 2q^{16} - 6q^{23} - 2q^{25} - 6q^{31} + 6q^{36} + 2q^{37} - 8q^{38} + 6q^{49} - 8q^{58} - 8q^{60} + 6q^{64} - 8q^{66} - 6q^{71} - 2q^{81} + 2q^{89} + 2q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2563, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2563.1.b.a $$1$$ $$1.279$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-2563})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}+q^{9}-q^{11}+q^{16}+q^{17}-q^{23}+\cdots$$
2563.1.b.b $$1$$ $$1.279$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-2563})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}+q^{9}+q^{11}+q^{16}-q^{17}-q^{23}+\cdots$$
2563.1.b.c $$2$$ $$1.279$$ $$\Q(\sqrt{-2})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}-\beta q^{3}-q^{4}+\beta q^{5}-2q^{6}+\cdots$$
2563.1.b.d $$2$$ $$1.279$$ $$\Q(\sqrt{-2})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}+\beta q^{3}-q^{4}-\beta q^{5}+2q^{6}+\cdots$$

## Hecke Characteristic Polynomials

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