# Properties

 Label 456.3.o Level $456$ Weight $3$ Character orbit 456.o Rep. character $\chi_{456}(265,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $1$ Sturm bound $240$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$456 = 2^{3} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 456.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(456, [\chi])$$.

Total New Old
Modular forms 168 20 148
Cusp forms 152 20 132
Eisenstein series 16 0 16

## Trace form

 $$20 q - 16 q^{7} - 60 q^{9} + O(q^{10})$$ $$20 q - 16 q^{7} - 60 q^{9} + 16 q^{11} + 32 q^{17} + 40 q^{19} + 64 q^{23} + 68 q^{25} - 208 q^{35} + 48 q^{39} + 64 q^{43} + 48 q^{47} + 20 q^{49} - 336 q^{55} - 60 q^{57} + 184 q^{61} + 48 q^{63} + 104 q^{73} + 88 q^{77} + 180 q^{81} + 224 q^{83} - 136 q^{85} - 240 q^{87} + 120 q^{93} - 320 q^{95} - 48 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(456, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
456.3.o.a $20$ $12.425$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\beta _{7}q^{3}-\beta _{4}q^{5}+(-1-\beta _{3})q^{7}-3q^{9}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(456, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(456, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 2}$$