# Properties

 Label 1710.2.l Level $1710$ Weight $2$ Character orbit 1710.l Rep. character $\chi_{1710}(1261,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $72$ Newform subspaces $19$ Sturm bound $720$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$19$$ Sturm bound: $$720$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1710, [\chi])$$.

Total New Old
Modular forms 752 72 680
Cusp forms 688 72 616
Eisenstein series 64 0 64

## Trace form

 $$72q - 2q^{2} - 36q^{4} + 4q^{8} + O(q^{10})$$ $$72q - 2q^{2} - 36q^{4} + 4q^{8} + 2q^{10} + 4q^{13} + 6q^{14} - 36q^{16} - 12q^{17} + 12q^{19} - 6q^{22} + 4q^{23} - 36q^{25} + 16q^{29} - 16q^{31} - 2q^{32} + 20q^{34} - 2q^{35} + 16q^{37} + 4q^{38} + 2q^{40} - 20q^{41} + 20q^{43} + 12q^{46} - 8q^{47} + 76q^{49} + 4q^{50} + 4q^{52} + 8q^{53} - 12q^{56} + 8q^{58} + 30q^{59} - 24q^{61} + 16q^{62} + 72q^{64} + 8q^{65} - 6q^{67} + 24q^{68} + 4q^{70} + 16q^{71} - 22q^{73} - 34q^{74} + 6q^{76} - 72q^{77} + 36q^{79} - 22q^{82} + 12q^{83} - 16q^{86} + 12q^{88} + 2q^{89} + 28q^{91} + 4q^{92} - 16q^{94} + 4q^{95} - 38q^{97} - 26q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1710, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1710.2.l.a $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.b $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.c $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$1$$ $$-10$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$$
1710.2.l.d $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$1$$ $$-10$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$$
1710.2.l.e $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$-10$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.f $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.g $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.h $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$2$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.i $$2$$ $$13.654$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$6$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
1710.2.l.j $$4$$ $$13.654$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$$
1710.2.l.k $$4$$ $$13.654$$ $$\Q(\sqrt{-3}, \sqrt{19})$$ None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$$
1710.2.l.l $$4$$ $$13.654$$ $$\Q(\sqrt{-3}, \sqrt{73})$$ None $$-2$$ $$0$$ $$2$$ $$-4$$ $$q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+(1-\beta _{2})q^{5}+\cdots$$
1710.2.l.m $$4$$ $$13.654$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-2$$ $$0$$ $$2$$ $$10$$ $$q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots$$
1710.2.l.n $$4$$ $$13.654$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$2$$ $$4$$ $$q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots$$
1710.2.l.o $$6$$ $$13.654$$ 6.0.29654208.1 None $$-3$$ $$0$$ $$-3$$ $$-6$$ $$q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$
1710.2.l.p $$6$$ $$13.654$$ 6.0.29654208.1 None $$3$$ $$0$$ $$3$$ $$-6$$ $$q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots$$
1710.2.l.q $$6$$ $$13.654$$ 6.0.29654208.1 None $$3$$ $$0$$ $$3$$ $$2$$ $$q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots$$
1710.2.l.r $$8$$ $$13.654$$ 8.0.4678560000.4 None $$-4$$ $$0$$ $$4$$ $$12$$ $$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots$$
1710.2.l.s $$8$$ $$13.654$$ 8.0.4678560000.4 None $$4$$ $$0$$ $$-4$$ $$12$$ $$q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1710, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1710, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(855, [\chi])$$$$^{\oplus 2}$$