# Properties

 Label 4000.1.bo Level 4000 Weight 1 Character orbit bo Rep. character $$\chi_{4000}(257,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 24 Newform subspaces 3 Sturm bound 600 Trace bound 37

# Related objects

## Defining parameters

 Level: $$N$$ = $$4000 = 2^{5} \cdot 5^{3}$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 4000.bo (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$25$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$3$$ Sturm bound: $$600$$ Trace bound: $$37$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(4000, [\chi])$$.

Total New Old
Modular forms 360 24 336
Cusp forms 40 24 16
Eisenstein series 320 0 320

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 0 0

## Trace form

 $$24q + O(q^{10})$$ $$24q - 2q^{13} - 2q^{17} + 2q^{37} + 2q^{53} + 2q^{73} + 6q^{81} + 10q^{89} + 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(4000, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4000.1.bo.a $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$D_{20}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots$$
4000.1.bo.b $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$D_{20}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots$$
4000.1.bo.c $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$D_{20}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(4000, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(4000, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(800, [\chi])$$$$^{\oplus 2}$$