# Properties

 Label 1008.2.s Level $1008$ Weight $2$ Character orbit 1008.s Rep. character $\chi_{1008}(289,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $38$ Newform subspaces $18$ 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.s (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$18$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 432 42 390
Cusp forms 336 38 298
Eisenstein series 96 4 92

## Trace form

 $$38q + q^{5} + O(q^{10})$$ $$38q + q^{5} - 3q^{11} - 4q^{13} + q^{17} + 9q^{19} - 9q^{23} - 20q^{25} + 4q^{29} - 9q^{31} - 15q^{35} + 3q^{37} - 4q^{41} + 16q^{43} + 15q^{47} + 6q^{49} + 9q^{53} + 22q^{55} - 11q^{59} + 3q^{61} + 18q^{65} + 7q^{67} + 8q^{71} + 11q^{73} - 25q^{77} + 13q^{79} + 64q^{83} - 10q^{85} - 3q^{89} + 52q^{91} + 45q^{95} + 4q^{97} + O(q^{100})$$

## 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.s.a $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$-5$$ $$q-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-3q^{13}+\cdots$$
1008.2.s.b $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$1$$ $$q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1008.2.s.c $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-1$$ $$q-2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
1008.2.s.d $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$5$$ $$q-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
1008.2.s.e $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-4$$ $$q-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$$
1008.2.s.f $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-1$$ $$q-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1008.2.s.g $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$4$$ $$q-\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1008.2.s.h $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$5$$ $$q-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
1008.2.s.i $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-5$$ $$q+(-2-\zeta_{6})q^{7}+5q^{13}-\zeta_{6}q^{19}+\cdots$$
1008.2.s.j $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+(2-3\zeta_{6})q^{7}-7q^{13}-7\zeta_{6}q^{19}+\cdots$$
1008.2.s.k $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-1$$ $$q+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
1008.2.s.l $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$5$$ $$q+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$$
1008.2.s.m $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-5$$ $$q+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
1008.2.s.n $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-5$$ $$q+3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1008.2.s.o $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$1$$ $$q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
1008.2.s.p $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$4$$ $$q+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
1008.2.s.q $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$4$$ $$-5$$ $$q+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-3q^{13}+\cdots$$
1008.2.s.r $$4$$ $$8.049$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$6$$ $$q+(-1+2\beta _{1}-\beta _{3})q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1008, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$