# Properties

 Label 1224.1.bv Level $1224$ Weight $1$ Character orbit 1224.bv Rep. character $\chi_{1224}(19,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $4$ Newform subspaces $1$ Sturm bound $216$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1224 = 2^{3} \cdot 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1224.bv (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$136$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$1$$ Sturm bound: $$216$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 48 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

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

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

## Trace form

 $$4q + O(q^{10})$$ $$4q + 4q^{11} - 4q^{16} + 4q^{43} - 4q^{50} + 4q^{59} - 4q^{82} - 4q^{83} - 4q^{88} - 4q^{97} + O(q^{100})$$

## 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.bv.a $$4$$ $$0.611$$ $$\Q(\zeta_{8})$$ $$D_{8}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(1-\zeta_{8}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1224, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1224, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(136, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

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