# Properties

 Label 510.2.f Level 510 Weight 2 Character orbit f Rep. character $$\chi_{510}(169,\cdot)$$ Character field $$\Q$$ Dimension 20 Newform subspaces 4 Sturm bound 216 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$510 = 2 \cdot 3 \cdot 5 \cdot 17$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 510.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$85$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$216$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(510, [\chi])$$.

Total New Old
Modular forms 116 20 96
Cusp forms 100 20 80
Eisenstein series 16 0 16

## Trace form

 $$20q - 20q^{4} + 20q^{9} + O(q^{10})$$ $$20q - 20q^{4} + 20q^{9} - 4q^{15} + 20q^{16} + 16q^{19} + 8q^{21} - 4q^{25} - 16q^{26} + 8q^{30} - 4q^{34} - 8q^{35} - 20q^{36} + 20q^{49} - 8q^{50} + 8q^{51} + 16q^{55} + 32q^{59} + 4q^{60} - 20q^{64} - 24q^{66} - 40q^{69} - 48q^{70} - 16q^{76} + 20q^{81} - 8q^{84} - 32q^{85} + 8q^{86} - 88q^{89} - 16q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(510, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
510.2.f.a $$4$$ $$4.072$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$-4$$ $$4$$ $$-8$$ $$q+\beta _{2}q^{2}-q^{3}-q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots$$
510.2.f.b $$4$$ $$4.072$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$4$$ $$-4$$ $$8$$ $$q+\beta _{2}q^{2}+q^{3}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots$$
510.2.f.c $$6$$ $$4.072$$ 6.0.350464.1 None $$0$$ $$-6$$ $$-2$$ $$4$$ $$q+\beta _{4}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$$
510.2.f.d $$6$$ $$4.072$$ 6.0.350464.1 None $$0$$ $$6$$ $$2$$ $$-4$$ $$q-\beta _{4}q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(510, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(510, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(85, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(170, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(255, [\chi])$$$$^{\oplus 2}$$