# Properties

 Label 1456.2.cc Level $1456$ Weight $2$ Character orbit 1456.cc Rep. character $\chi_{1456}(225,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $84$ Newform subspaces $7$ Sturm bound $448$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1456 = 2^{4} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1456.cc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$7$$ Sturm bound: $$448$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 472 84 388
Cusp forms 424 84 340
Eisenstein series 48 0 48

## Trace form

 $$84 q - 42 q^{9} + O(q^{10})$$ $$84 q - 42 q^{9} - 2 q^{13} - 2 q^{17} + 12 q^{23} - 88 q^{25} - 24 q^{27} + 2 q^{29} + 12 q^{35} + 30 q^{37} + 12 q^{39} + 6 q^{41} - 28 q^{43} - 30 q^{45} + 42 q^{49} + 72 q^{51} + 4 q^{53} + 40 q^{55} + 36 q^{59} - 10 q^{61} + 6 q^{65} - 72 q^{67} - 36 q^{71} - 16 q^{75} + 16 q^{79} - 34 q^{81} - 6 q^{85} - 36 q^{87} + 24 q^{89} + 24 q^{95} - 24 q^{97} + O(q^{100})$$

## 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.cc.a $4$ $11.626$ $$\Q(\zeta_{12})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-2+2\zeta_{12}^{2})q^{3}+(1-2\zeta_{12}^{2})q^{5}+\cdots$$
1456.2.cc.b $4$ $11.626$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{3}q^{5}+\cdots$$
1456.2.cc.c $12$ $11.626$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{10})q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots$$
1456.2.cc.d $12$ $11.626$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{10}q^{3}+(-\beta _{1}+\beta _{5}-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$$
1456.2.cc.e $12$ $11.626$ 12.0.$$\cdots$$.1 None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{8})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{6}+\cdots)q^{5}+\cdots$$
1456.2.cc.f $16$ $11.626$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2}-\beta _{14})q^{3}+(\beta _{2}+\beta _{12}+\cdots)q^{5}+\cdots$$
1456.2.cc.g $24$ $11.626$ None $$0$$ $$2$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(1456, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(364, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(728, [\chi])$$$$^{\oplus 2}$$