# Properties

 Label 1224.1.cx Level $1224$ Weight $1$ Character orbit 1224.cx Rep. character $\chi_{1224}(11,\cdot)$ Character field $\Q(\zeta_{48})$ Dimension $32$ Newform subspaces $2$ Sturm bound $216$ Trace bound $12$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1224 = 2^{3} \cdot 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1224.cx (of order $$48$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1224$$ Character field: $$\Q(\zeta_{48})$$ Newform subspaces: $$2$$ Sturm bound: $$216$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1224, [\chi])$$.

Total New Old
Modular forms 96 96 0
Cusp forms 32 32 0
Eisenstein series 64 64 0

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

 $$32q + O(q^{10})$$ $$32q - 16q^{12} + 8q^{24} - 24q^{38} - 8q^{43} - 8q^{54} + 8q^{57} - 8q^{66} + 8q^{81} - 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1224, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1224.1.cx.a $$16$$ $$0.611$$ $$\Q(\zeta_{48})$$ $$D_{48}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{48}^{5}q^{2}+\zeta_{48}^{14}q^{3}+\zeta_{48}^{10}q^{4}+\cdots$$
1224.1.cx.b $$16$$ $$0.611$$ $$\Q(\zeta_{48})$$ $$D_{48}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{48}^{5}q^{2}+\zeta_{48}^{17}q^{3}+\zeta_{48}^{10}q^{4}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - T^{8} + T^{16}$$)($$1 - T^{8} + T^{16}$$)
$3$ ($$( 1 - T^{4} + T^{8} )^{2}$$)($$1 - T^{8} + T^{16}$$)
$5$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$7$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$11$ ($$( 1 + T^{2} )^{8}( 1 - T^{8} + T^{16} )$$)($$( 1 - T^{2} + T^{4} )^{4}( 1 + T^{8} )^{2}$$)
$13$ ($$( 1 - T^{4} + T^{8} )^{4}$$)($$( 1 - T^{4} + T^{8} )^{4}$$)
$17$ ($$1 - T^{8} + T^{16}$$)($$1 - T^{8} + T^{16}$$)
$19$ ($$( 1 - T^{8} + T^{16} )^{2}$$)($$( 1 - T^{8} + T^{16} )^{2}$$)
$23$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$29$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$31$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$37$ ($$( 1 + T^{16} )^{2}$$)($$( 1 + T^{16} )^{2}$$)
$41$ ($$( 1 - T^{4} + T^{8} )^{2}( 1 + T^{8} )^{2}$$)($$( 1 + T^{4} )^{4}( 1 - T^{8} + T^{16} )$$)
$43$ ($$( 1 - T + T^{2} )^{8}( 1 + T^{4} )^{4}$$)($$( 1 + T )^{16}( 1 - T^{4} + T^{8} )^{2}$$)
$47$ ($$( 1 - T^{4} + T^{8} )^{4}$$)($$( 1 - T^{4} + T^{8} )^{4}$$)
$53$ ($$( 1 + T^{8} )^{4}$$)($$( 1 + T^{8} )^{4}$$)
$59$ ($$( 1 - T^{2} + T^{4} )^{4}( 1 + T^{4} )^{4}$$)($$( 1 + T^{2} )^{8}( 1 - T^{4} + T^{8} )^{2}$$)
$61$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$67$ ($$( 1 + T^{8} )^{2}( 1 - T^{8} + T^{16} )$$)($$( 1 + T^{8} )^{2}( 1 - T^{8} + T^{16} )$$)
$71$ ($$( 1 + T^{16} )^{2}$$)($$( 1 + T^{16} )^{2}$$)
$73$ ($$( 1 - T^{4} + T^{8} )^{2}( 1 - T^{8} + T^{16} )$$)($$( 1 - T^{4} + T^{8} )^{2}( 1 - T^{8} + T^{16} )$$)
$79$ ($$1 - T^{16} + T^{32}$$)($$1 - T^{16} + T^{32}$$)
$83$ ($$( 1 - T + T^{2} )^{8}( 1 - T^{4} + T^{8} )^{2}$$)($$( 1 + T + T^{2} )^{8}( 1 - T^{4} + T^{8} )^{2}$$)
$89$ ($$( 1 + T^{8} )^{4}$$)($$( 1 + T^{8} )^{4}$$)
$97$ ($$( 1 - T^{2} + T^{4} )^{4}( 1 + T^{8} )^{2}$$)($$( 1 + T^{2} )^{8}( 1 - T^{8} + T^{16} )$$)