# Properties

 Label 456.2.bf Level $456$ Weight $2$ Character orbit 456.bf Rep. character $\chi_{456}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $4$ Sturm bound $160$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$456 = 2^{3} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 456.bf (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$160$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(456, [\chi])$$.

Total New Old
Modular forms 176 40 136
Cusp forms 144 40 104
Eisenstein series 32 0 32

## Trace form

 $$40 q + 3 q^{3} + 4 q^{7} + 3 q^{9} + O(q^{10})$$ $$40 q + 3 q^{3} + 4 q^{7} + 3 q^{9} - 6 q^{13} + 12 q^{15} - 10 q^{19} + 16 q^{25} + 9 q^{33} + 4 q^{39} + 2 q^{43} + 40 q^{45} + 28 q^{49} - 18 q^{51} - 12 q^{55} - 22 q^{57} + 2 q^{61} - 20 q^{63} - 12 q^{67} + 4 q^{73} - 54 q^{79} - 13 q^{81} + 4 q^{85} - 8 q^{87} - 90 q^{91} - 18 q^{93} - 66 q^{97} - 25 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(456, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
456.2.bf.a $4$ $3.641$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$1$$ $$-3$$ $$2$$ $$q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
456.2.bf.b $4$ $3.641$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$2$$ $$3$$ $$2$$ $$q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots$$
456.2.bf.c $16$ $3.641$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-1$$ $$-3$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{14}q^{5}+(\beta _{5}-\beta _{13})q^{7}+\cdots$$
456.2.bf.d $16$ $3.641$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$1$$ $$3$$ $$0$$ $$q+\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(\beta _{5}-\beta _{13}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(456, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(456, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 2}$$