# Properties

 Label 1224.1.cp Level $1224$ Weight $1$ Character orbit 1224.cp Rep. character $\chi_{1224}(43,\cdot)$ Character field $\Q(\zeta_{24})$ Dimension $16$ Newform subspaces $2$ Sturm bound $216$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1224 = 2^{3} \cdot 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1224.cp (of order $$24$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1224$$ Character field: $$\Q(\zeta_{24})$$ Newform subspaces: $$2$$ Sturm bound: $$216$$ Trace bound: $$9$$

## Dimensions

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

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16q + 4q^{9} + O(q^{10})$$ $$16q + 4q^{9} - 4q^{11} + 8q^{12} + 8q^{16} - 4q^{24} + 4q^{36} + 4q^{43} - 8q^{50} - 4q^{54} - 12q^{57} - 4q^{59} - 4q^{66} + 4q^{75} + 8q^{82} - 8q^{83} - 4q^{88} - 4q^{97} - 4q^{99} + O(q^{100})$$

## 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.cp.a $$8$$ $$0.611$$ $$\Q(\zeta_{24})$$ $$D_{24}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{2}q^{6}+\cdots$$
1224.1.cp.b $$8$$ $$0.611$$ $$\Q(\zeta_{24})$$ $$D_{24}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{2}-\zeta_{24}^{10}q^{3}+\zeta_{24}^{2}q^{4}+\cdots$$

## Hecke characteristic polynomials

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