# Properties

 Label 900.3.ba Level $900$ Weight $3$ Character orbit 900.ba Rep. character $\chi_{900}(161,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $80$ Newform subspaces $1$ Sturm bound $540$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.ba (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$75$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$540$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(900, [\chi])$$.

Total New Old
Modular forms 1488 80 1408
Cusp forms 1392 80 1312
Eisenstein series 96 0 96

## Trace form

 $$80q + 16q^{7} + O(q^{10})$$ $$80q + 16q^{7} - 8q^{13} + 60q^{19} - 120q^{25} + 120q^{31} + 116q^{37} - 80q^{43} + 440q^{49} + 120q^{55} + 80q^{61} + 24q^{67} + 128q^{73} + 40q^{79} + 40q^{85} - 140q^{91} + 384q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(900, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
900.3.ba.a $$80$$ $$24.523$$ None $$0$$ $$0$$ $$0$$ $$16$$

## Decomposition of $$S_{3}^{\mathrm{old}}(900, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$