# Properties

 Label 1170.2.bs Level $1170$ Weight $2$ Character orbit 1170.bs Rep. character $\chi_{1170}(361,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $44$ Newform subspaces $8$ Sturm bound $504$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.bs (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$504$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1170, [\chi])$$.

Total New Old
Modular forms 536 44 492
Cusp forms 472 44 428
Eisenstein series 64 0 64

## Trace form

 $$44q + 22q^{4} + O(q^{10})$$ $$44q + 22q^{4} + 2q^{10} - 6q^{11} + 12q^{13} - 12q^{14} - 22q^{16} - 16q^{17} - 18q^{19} - 44q^{25} + 16q^{26} - 4q^{29} + 2q^{35} + 36q^{37} + 24q^{38} + 4q^{40} + 24q^{41} - 12q^{46} + 28q^{49} - 32q^{53} - 12q^{55} - 6q^{56} + 12q^{58} - 36q^{59} + 8q^{61} - 32q^{62} - 44q^{64} + 14q^{65} + 72q^{67} + 16q^{68} + 72q^{71} - 22q^{74} - 18q^{76} + 8q^{77} + 8q^{79} + 16q^{82} - 36q^{85} + 30q^{89} + 38q^{91} - 10q^{94} - 16q^{95} - 12q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1170, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1170.2.bs.a $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-6$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+(-2+\cdots)q^{7}+\cdots$$
1170.2.bs.b $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$$
1170.2.bs.c $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1170.2.bs.d $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1170.2.bs.e $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1170.2.bs.f $$8$$ $$9.342$$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{5})q^{2}+\beta _{6}q^{4}-\beta _{2}q^{5}+\cdots$$
1170.2.bs.g $$8$$ $$9.342$$ 8.0.22581504.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1-\beta _{4})q^{4}+(-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$$
1170.2.bs.h $$8$$ $$9.342$$ 8.0.1731891456.1 None $$0$$ $$0$$ $$0$$ $$6$$ $$q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}-\beta _{5}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1170, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1170, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(234, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(585, [\chi])$$$$^{\oplus 2}$$