# Properties

 Label 456.2.f Level $456$ Weight $2$ Character orbit 456.f Rep. character $\chi_{456}(113,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $2$ 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.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$160$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$29$$

## Dimensions

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

Total New Old
Modular forms 88 20 68
Cusp forms 72 20 52
Eisenstein series 16 0 16

## Trace form

 $$20 q - 4 q^{7} + 6 q^{9} + O(q^{10})$$ $$20 q - 4 q^{7} + 6 q^{9} + 4 q^{19} - 28 q^{25} + 14 q^{39} + 40 q^{43} - 4 q^{45} + 32 q^{49} - 24 q^{55} - 2 q^{57} - 8 q^{61} - 34 q^{63} - 52 q^{73} + 46 q^{81} - 16 q^{85} + 26 q^{87} - 36 q^{93} + 4 q^{99} + O(q^{100})$$

## 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.f.a $10$ $3.641$ 10.0.$$\cdots$$.1 None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q+\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots$$
456.2.f.b $10$ $3.641$ 10.0.$$\cdots$$.1 None $$0$$ $$1$$ $$0$$ $$-2$$ $$q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots$$

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

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