# Properties

 Label 1456.2.k Level $1456$ Weight $2$ Character orbit 1456.k Rep. character $\chi_{1456}(337,\cdot)$ Character field $\Q$ Dimension $42$ Newform subspaces $6$ Sturm bound $448$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1456 = 2^{4} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1456.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$448$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1456, [\chi])$$.

Total New Old
Modular forms 236 42 194
Cusp forms 212 42 170
Eisenstein series 24 0 24

## Trace form

 $$42 q + 42 q^{9} + O(q^{10})$$ $$42 q + 42 q^{9} + 2 q^{13} - 4 q^{17} - 12 q^{23} - 38 q^{25} + 24 q^{27} + 4 q^{29} - 12 q^{35} + 24 q^{39} + 28 q^{43} - 42 q^{49} - 4 q^{53} + 32 q^{55} - 20 q^{61} + 16 q^{75} + 44 q^{79} + 58 q^{81} - 72 q^{87} - 84 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1456, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1456.2.k.a $2$ $11.626$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+2iq^{5}-iq^{7}-2q^{9}-5iq^{11}+\cdots$$
1456.2.k.b $6$ $11.626$ 6.0.30647296.1 None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots$$
1456.2.k.c $6$ $11.626$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots$$
1456.2.k.d $8$ $11.626$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{3}+\beta _{4})q^{5}+\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots$$
1456.2.k.e $8$ $11.626$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots$$
1456.2.k.f $12$ $11.626$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{5}-\beta _{7})q^{5}-\beta _{4}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1456, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1456, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(364, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(728, [\chi])$$$$^{\oplus 2}$$