# Properties

 Label 1456.2.r Level $1456$ Weight $2$ Character orbit 1456.r Rep. character $\chi_{1456}(417,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $96$ Newform subspaces $18$ Sturm bound $448$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1456 = 2^{4} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1456.r (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$18$$ Sturm bound: $$448$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$5$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 472 96 376
Cusp forms 424 96 328
Eisenstein series 48 0 48

## Trace form

 $$96 q - 48 q^{9} + O(q^{10})$$ $$96 q - 48 q^{9} + 4 q^{11} - 12 q^{19} + 8 q^{21} + 16 q^{23} - 56 q^{25} + 32 q^{29} + 12 q^{31} - 8 q^{33} + 36 q^{35} - 8 q^{37} - 8 q^{43} - 8 q^{45} + 8 q^{47} + 8 q^{49} - 20 q^{51} - 12 q^{53} - 24 q^{55} - 36 q^{59} - 4 q^{61} - 76 q^{63} + 8 q^{67} - 32 q^{69} - 8 q^{71} + 16 q^{73} + 36 q^{75} + 4 q^{77} + 20 q^{79} - 40 q^{81} + 88 q^{83} - 32 q^{85} + 36 q^{87} + 8 q^{89} + 16 q^{93} + 12 q^{95} - 16 q^{97} - 112 q^{99} + O(q^{100})$$

## 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.r.a $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$3$$ $$4$$ $$q+(-3+3\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
1456.2.r.b $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$-5$$ $$q+(-2+2\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
1456.2.r.c $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$-4$$ $$q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
1456.2.r.d $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1456.2.r.e $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$3$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1456.2.r.f $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-5$$ $$q+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1-\zeta_{6})q^{11}+\cdots$$
1456.2.r.g $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots$$
1456.2.r.h $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$-4$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
1456.2.r.i $2$ $11.626$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$3$$ $$4$$ $$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
1456.2.r.j $4$ $11.626$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(3+2\beta _{1})q^{7}+\cdots$$
1456.2.r.k $4$ $11.626$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(2+2\beta _{2})q^{3}+(\beta _{1}+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$$
1456.2.r.l $6$ $11.626$ 6.0.309123.1 None $$0$$ $$0$$ $$2$$ $$4$$ $$q+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{5})q^{3}+(1-\beta _{4}+\cdots)q^{5}+\cdots$$
1456.2.r.m $8$ $11.626$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$q+(\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots$$
1456.2.r.n $8$ $11.626$ 8.0.8681953329.1 None $$0$$ $$0$$ $$-2$$ $$-7$$ $$q+(\beta _{1}+\beta _{7})q^{3}+(-\beta _{2}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$$
1456.2.r.o $8$ $11.626$ 8.0.856615824.2 None $$0$$ $$3$$ $$1$$ $$-1$$ $$q+(\beta _{1}-\beta _{2}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$$
1456.2.r.p $10$ $11.626$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$-1$$ $$q-\beta _{9}q^{3}+(-\beta _{3}-\beta _{7})q^{5}+(\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots$$
1456.2.r.q $14$ $11.626$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$-2$$ $$-2$$ $$2$$ $$q-\beta _{1}q^{3}-\beta _{9}q^{5}+\beta _{4}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$$
1456.2.r.r $16$ $11.626$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$2$$ $$0$$ $$-1$$ $$q+\beta _{1}q^{3}+(\beta _{4}+\beta _{10})q^{5}+(\beta _{5}-\beta _{12}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1456, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(364, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(728, [\chi])$$$$^{\oplus 2}$$