# Properties

 Label 224.1.r Level 224 Weight 1 Character orbit r Rep. character $$\chi_{224}(95,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 4 Newform subspaces 1 Sturm bound 32 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 224.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(224, [\chi])$$.

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

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

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

## Trace form

 $$4q - 2q^{5} + O(q^{10})$$ $$4q - 2q^{5} - 2q^{17} - 2q^{21} - 2q^{33} + 2q^{37} - 4q^{49} + 2q^{53} - 4q^{57} + 2q^{61} + 4q^{69} + 2q^{73} + 2q^{77} + 2q^{81} + 4q^{85} + 2q^{89} - 2q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(224, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
224.1.r.a $$4$$ $$0.112$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$

## Hecke characteristic polynomials

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