# Properties

 Label 1008.2.bt Level $1008$ Weight $2$ Character orbit 1008.bt Rep. character $\chi_{1008}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $4$ Sturm bound $384$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.bt (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1008, [\chi])$$.

Total New Old
Modular forms 432 32 400
Cusp forms 336 32 304
Eisenstein series 96 0 96

## Trace form

 $$32 q + 4 q^{7} + O(q^{10})$$ $$32 q + 4 q^{7} - 12 q^{19} - 8 q^{25} - 12 q^{31} + 8 q^{43} - 4 q^{67} + 24 q^{73} + 36 q^{79} - 32 q^{85} + 36 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1008, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.2.bt.a $4$ $8.049$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{2}q^{5}+(-2+3\beta _{1})q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots$$
1008.2.bt.b $4$ $8.049$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(-\beta _{1}-\beta _{3})q^{5}+(2-3\beta _{2})q^{7}+\beta _{1}q^{11}+\cdots$$
1008.2.bt.c $8$ $8.049$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}+(-\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots$$
1008.2.bt.d $16$ $8.049$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(\beta _{4}-\beta _{10})q^{5}+(\beta _{3}+\beta _{9})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1008, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1008, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$