# Properties

 Label 1710.2.d Level $1710$ Weight $2$ Character orbit 1710.d Rep. character $\chi_{1710}(1369,\cdot)$ Character field $\Q$ Dimension $46$ Newform subspaces $8$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$720$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 376 46 330
Cusp forms 344 46 298
Eisenstein series 32 0 32

## Trace form

 $$46 q - 46 q^{4} - 6 q^{5} + O(q^{10})$$ $$46 q - 46 q^{4} - 6 q^{5} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 46 q^{16} - 2 q^{19} + 6 q^{20} - 18 q^{25} - 20 q^{26} + 4 q^{29} + 16 q^{31} - 20 q^{35} - 4 q^{40} + 12 q^{41} - 8 q^{44} - 4 q^{46} - 46 q^{49} + 8 q^{50} - 8 q^{55} + 4 q^{56} + 24 q^{59} + 4 q^{61} - 46 q^{64} - 44 q^{65} + 16 q^{70} + 32 q^{71} + 12 q^{74} + 2 q^{76} + 24 q^{79} - 6 q^{80} + 4 q^{85} + 20 q^{86} + 20 q^{89} - 64 q^{91} + 12 q^{94} - 2 q^{95} + O(q^{100})$$

## 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.d.a $2$ $13.654$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-q^{4}+(-2+i)q^{5}-iq^{8}+\cdots$$
1710.2.d.b $2$ $13.654$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{2}-q^{4}+(1+2i)q^{5}+iq^{8}+(2+\cdots)q^{10}+\cdots$$
1710.2.d.c $4$ $13.654$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$$
1710.2.d.d $6$ $13.654$ 6.0.5161984.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$$
1710.2.d.e $6$ $13.654$ 6.0.350464.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$$
1710.2.d.f $6$ $13.654$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$$
1710.2.d.g $8$ $13.654$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}+\cdots)q^{7}+\cdots$$
1710.2.d.h $12$ $13.654$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{3}q^{8}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(855, [\chi])$$$$^{\oplus 2}$$