# Properties

 Label 1064.2.q Level $1064$ Weight $2$ Character orbit 1064.q Rep. character $\chi_{1064}(305,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $72$ Newform subspaces $15$ Sturm bound $320$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1064 = 2^{3} \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1064.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$15$$ Sturm bound: $$320$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1064, [\chi])$$.

Total New Old
Modular forms 336 72 264
Cusp forms 304 72 232
Eisenstein series 32 0 32

## Trace form

 $$72 q - 4 q^{5} - 4 q^{7} - 32 q^{9} + O(q^{10})$$ $$72 q - 4 q^{5} - 4 q^{7} - 32 q^{9} - 8 q^{15} - 8 q^{17} + 6 q^{19} + 12 q^{21} - 6 q^{23} - 48 q^{25} - 24 q^{27} + 24 q^{29} + 4 q^{31} - 4 q^{33} + 12 q^{35} + 30 q^{39} - 8 q^{41} + 16 q^{43} - 24 q^{45} + 6 q^{47} + 28 q^{51} - 8 q^{53} - 4 q^{55} + 10 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} - 80 q^{71} + 16 q^{73} - 8 q^{75} - 26 q^{77} + 16 q^{79} - 44 q^{81} - 76 q^{83} + 44 q^{85} - 28 q^{87} - 4 q^{89} - 40 q^{93} + 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1064, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1064.2.q.a $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$-5$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
1064.2.q.b $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$-5$$ $$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
1064.2.q.c $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$5$$ $$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1064.2.q.d $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-1$$ $$q-3\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
1064.2.q.e $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$5$$ $$q-3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots$$
1064.2.q.f $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-5$$ $$q-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
1064.2.q.g $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$5$$ $$q+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$$
1064.2.q.h $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$-1$$ $$q+(2-2\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
1064.2.q.i $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$1$$ $$-1$$ $$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$$
1064.2.q.j $2$ $8.496$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$1$$ $$4$$ $$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1064.2.q.k $4$ $8.496$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-4$$ $$2$$ $$2$$ $$q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2})q^{5}+\cdots$$
1064.2.q.l $4$ $8.496$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$4$$ $$2$$ $$-3$$ $$q+2\beta _{2}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots$$
1064.2.q.m $6$ $8.496$ 6.0.31259952.1 None $$0$$ $$0$$ $$-2$$ $$-3$$ $$q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots$$
1064.2.q.n $16$ $8.496$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$1$$ $$5$$ $$q+\beta _{1}q^{3}+\beta _{10}q^{5}+\beta _{11}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$$
1064.2.q.o $22$ $8.496$ None $$0$$ $$0$$ $$-3$$ $$-6$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1064, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1064, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(133, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(266, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(532, [\chi])$$$$^{\oplus 2}$$