# Properties

 Label 1170.2.e Level $1170$ Weight $2$ Character orbit 1170.e Rep. character $\chi_{1170}(469,\cdot)$ Character field $\Q$ Dimension $30$ Newform subspaces $8$ Sturm bound $504$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$504$$ Trace bound: $$11$$ 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 268 30 238
Cusp forms 236 30 206
Eisenstein series 32 0 32

## Trace form

 $$30 q - 30 q^{4} - 8 q^{5} + O(q^{10})$$ $$30 q - 30 q^{4} - 8 q^{5} + 4 q^{10} + 4 q^{11} - 4 q^{14} + 30 q^{16} - 4 q^{19} + 8 q^{20} - 8 q^{25} - 6 q^{26} - 4 q^{29} + 8 q^{31} - 8 q^{34} + 30 q^{35} - 4 q^{40} - 20 q^{41} - 4 q^{44} - 20 q^{46} - 18 q^{49} + 16 q^{50} + 16 q^{55} + 4 q^{56} - 12 q^{59} - 28 q^{61} - 30 q^{64} + 4 q^{65} + 28 q^{70} + 16 q^{71} + 4 q^{76} + 8 q^{79} - 8 q^{80} + 12 q^{85} - 8 q^{86} - 36 q^{89} + 12 q^{91} + 20 q^{94} - 20 q^{95} + O(q^{100})$$

## 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.e.a $2$ $9.342$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots$$
1170.2.e.b $2$ $9.342$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-iq^{2}-q^{4}+(-2+i)q^{5}+4iq^{7}+\cdots$$
1170.2.e.c $2$ $9.342$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-q^{4}+(-2-i)q^{5}+4iq^{7}+\cdots$$
1170.2.e.d $2$ $9.342$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-iq^{2}-q^{4}+(2+i)q^{5}+iq^{8}+(1+\cdots)q^{10}+\cdots$$
1170.2.e.e $4$ $9.342$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
1170.2.e.f $6$ $9.342$ 6.0.3534400.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$$
1170.2.e.g $6$ $9.342$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}-q^{4}+(-\beta _{2}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1170.2.e.h $6$ $9.342$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-q^{4}+(\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1170, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(585, [\chi])$$$$^{\oplus 2}$$