# Properties

 Label 4020.2.f Level 4020 Weight 2 Character orbit f Rep. character $$\chi_{4020}(401,\cdot)$$ Character field $$\Q$$ Dimension 92 Newform subspaces 2 Sturm bound 1632 Trace bound 5

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## Defining parameters

 Level: $$N$$ = $$4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4020.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$1632$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4020, [\chi])$$.

Total New Old
Modular forms 828 92 736
Cusp forms 804 92 712
Eisenstein series 24 0 24

## Trace form

 $$92q - 8q^{9} + O(q^{10})$$ $$92q - 8q^{9} + 16q^{19} + 92q^{25} + 8q^{33} - 16q^{37} - 24q^{39} - 124q^{49} - 28q^{67} - 80q^{73} - 24q^{81} - 8q^{91} + 4q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4020, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4020.2.f.a $$46$$ $$32.100$$ None $$0$$ $$0$$ $$-46$$ $$0$$
4020.2.f.b $$46$$ $$32.100$$ None $$0$$ $$0$$ $$46$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4020, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4020, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(201, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(402, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(804, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1005, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2010, [\chi])$$$$^{\oplus 2}$$