# Properties

 Label 1170.2.i Level $1170$ Weight $2$ Character orbit 1170.i Rep. character $\chi_{1170}(451,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $44$ Newform subspaces $17$ 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.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$17$$ Sturm bound: $$504$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$29$$

## 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

 $$44q - 22q^{4} + 8q^{7} + O(q^{10})$$ $$44q - 22q^{4} + 8q^{7} + 2q^{10} - 14q^{11} - 4q^{13} - 4q^{14} - 22q^{16} - 8q^{17} - 6q^{19} + 8q^{22} - 8q^{23} + 44q^{25} - 8q^{26} + 8q^{28} + 20q^{29} - 8q^{31} + 16q^{34} - 6q^{35} + 4q^{37} + 24q^{38} - 4q^{40} + 20q^{41} + 16q^{43} + 28q^{44} + 16q^{46} + 16q^{47} - 12q^{49} + 8q^{52} - 16q^{53} - 4q^{55} + 2q^{56} - 20q^{58} + 16q^{59} - 24q^{61} + 44q^{64} - 10q^{65} - 16q^{67} - 8q^{68} + 56q^{73} + 2q^{74} - 6q^{76} + 24q^{77} + 104q^{79} - 48q^{83} - 12q^{85} - 56q^{86} + 8q^{88} - 46q^{89} + 106q^{91} + 16q^{92} - 2q^{94} - 44q^{97} - 32q^{98} + O(q^{100})$$

## 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.i.a $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-2$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+2\zeta_{6}q^{7}+\cdots$$
1170.2.i.b $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-2$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+4\zeta_{6}q^{7}+\cdots$$
1170.2.i.c $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$-3$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-3\zeta_{6}q^{7}+\cdots$$
1170.2.i.d $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots$$
1170.2.i.e $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}+\cdots$$
1170.2.i.f $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+\cdots$$
1170.2.i.g $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$5$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+5\zeta_{6}q^{7}+\cdots$$
1170.2.i.h $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$0$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$$
1170.2.i.i $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$3$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots$$
1170.2.i.j $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$3$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots$$
1170.2.i.k $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$2$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots$$
1170.2.i.l $$2$$ $$9.342$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$2$$ $$4$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots$$
1170.2.i.m $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$-4$$ $$-4$$ $$q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}-q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots$$
1170.2.i.n $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$-4$$ $$2$$ $$q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}-q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots$$
1170.2.i.o $$4$$ $$9.342$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$2$$ $$0$$ $$-4$$ $$-3$$ $$q+(1-\beta _{2})q^{2}-\beta _{2}q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1170.2.i.p $$4$$ $$9.342$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$4$$ $$-4$$ $$q+(1-\zeta_{12})q^{2}-\zeta_{12}q^{4}+q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots$$
1170.2.i.q $$4$$ $$9.342$$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$2$$ $$0$$ $$4$$ $$2$$ $$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+q^{5}-\beta _{2}q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1170, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(234, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(585, [\chi])$$$$^{\oplus 2}$$