# Properties

 Label 1170.2.bj Level $1170$ Weight $2$ Character orbit 1170.bj Rep. character $\chi_{1170}(199,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $6$ Sturm bound $504$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.bj (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$504$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 536 72 464
Cusp forms 472 72 400
Eisenstein series 64 0 64

## Trace form

 $$72 q - 36 q^{4} + O(q^{10})$$ $$72 q - 36 q^{4} - q^{10} - 6 q^{11} + 12 q^{14} - 36 q^{16} - 30 q^{19} - 3 q^{20} - 2 q^{25} + 2 q^{26} - 22 q^{29} + 14 q^{35} + 2 q^{40} - 6 q^{41} - 12 q^{46} - 26 q^{49} + 27 q^{50} + 16 q^{55} - 6 q^{56} + 12 q^{59} - 22 q^{61} + 72 q^{64} + 23 q^{65} + 24 q^{71} - 16 q^{74} + 30 q^{76} + 56 q^{79} + 3 q^{80} - 33 q^{85} + 42 q^{89} - 50 q^{91} + 26 q^{94} + O(q^{100})$$

## 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.bj.a $8$ $9.342$ 8.0.$$\cdots$$.1 None $$-4$$ $$0$$ $$3$$ $$-5$$ $$q+(-1+\beta _{3})q^{2}-\beta _{3}q^{4}+\beta _{6}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
1170.2.bj.b $8$ $9.342$ 8.0.$$\cdots$$.1 None $$4$$ $$0$$ $$-3$$ $$5$$ $$q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}-\beta _{6}q^{5}+(2+\cdots)q^{7}+\cdots$$
1170.2.bj.c $12$ $9.342$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$0$$ $$-2$$ $$2$$ $$q+(-1-\beta _{4})q^{2}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
1170.2.bj.d $12$ $9.342$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$0$$ $$2$$ $$-2$$ $$q+(1+\beta _{4})q^{2}+\beta _{4}q^{4}+(-\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$$
1170.2.bj.e $16$ $9.342$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{2}+(-1-\beta _{7})q^{4}-\beta _{2}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots$$
1170.2.bj.f $16$ $9.342$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+(-1-\beta _{7})q^{4}+\beta _{2}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1170, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(585, [\chi])$$$$^{\oplus 2}$$