# Properties

 Label 456.2.q Level $456$ Weight $2$ Character orbit 456.q Rep. character $\chi_{456}(49,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $20$ Newform subspaces $6$ Sturm bound $160$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$456 = 2^{3} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 456.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ Sturm bound: $$160$$ Trace bound: $$5$$ 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 20 156
Cusp forms 144 20 124
Eisenstein series 32 0 32

## Trace form

 $$20 q + 2 q^{3} + 4 q^{7} - 10 q^{9} + O(q^{10})$$ $$20 q + 2 q^{3} + 4 q^{7} - 10 q^{9} - 8 q^{11} - 6 q^{13} + 4 q^{17} - 8 q^{19} - 6 q^{21} + 4 q^{23} - 6 q^{25} - 4 q^{27} + 4 q^{29} + 20 q^{31} - 4 q^{33} + 24 q^{35} + 20 q^{37} + 4 q^{39} - 8 q^{41} + 6 q^{43} + 12 q^{47} + 56 q^{49} + 12 q^{51} - 20 q^{53} - 16 q^{55} + 10 q^{57} - 18 q^{61} - 2 q^{63} - 48 q^{65} - 2 q^{67} + 8 q^{69} - 16 q^{71} - 18 q^{73} - 28 q^{75} - 8 q^{77} - 2 q^{79} - 10 q^{81} - 88 q^{83} - 56 q^{87} - 24 q^{89} + 58 q^{91} + 18 q^{93} - 8 q^{95} - 12 q^{97} + 4 q^{99} + O(q^{100})$$

## 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.q.a $2$ $3.641$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$-6$$ $$q+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-3q^{7}+\cdots$$
456.2.q.b $2$ $3.641$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$6$$ $$q+(-1+\zeta_{6})q^{3}+3q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots$$
456.2.q.c $2$ $3.641$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$2$$ $$-10$$ $$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-5q^{7}+\cdots$$
456.2.q.d $4$ $3.641$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$0$$ $$-2$$ $$2$$ $$8$$ $$q+(-1-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots$$
456.2.q.e $4$ $3.641$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$0$$ $$2$$ $$-2$$ $$0$$ $$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$$
456.2.q.f $6$ $3.641$ $$\Q(\zeta_{18})$$ None $$0$$ $$3$$ $$0$$ $$6$$ $$q+\zeta_{18}q^{3}+\zeta_{18}^{2}q^{5}+(1+\zeta_{18}^{5})q^{7}+\cdots$$

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

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