# Properties

 Label 900.3.g Level $900$ Weight $3$ Character orbit 900.g Rep. character $\chi_{900}(701,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $4$ Sturm bound $540$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$540$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 396 12 384
Cusp forms 324 12 312
Eisenstein series 72 0 72

## Trace form

 $$12q + 16q^{7} + O(q^{10})$$ $$12q + 16q^{7} - 8q^{13} - 44q^{19} - 76q^{31} + 136q^{37} - 80q^{43} + 24q^{49} - 60q^{61} + 304q^{67} - 152q^{73} - 80q^{79} - 196q^{91} + 424q^{97} + O(q^{100})$$

## 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.g.a $$2$$ $$24.523$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-q^{7}+\beta q^{11}-7q^{13}-\beta q^{17}-7q^{19}+\cdots$$
900.3.g.b $$2$$ $$24.523$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+q^{7}+\beta q^{11}+7q^{13}+\beta q^{17}-7q^{19}+\cdots$$
900.3.g.c $$4$$ $$24.523$$ $$\Q(\sqrt{-2}, \sqrt{-23})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{7}-7\beta _{1}q^{11}+3\beta _{2}q^{13}-2\beta _{3}q^{17}+\cdots$$
900.3.g.d $$4$$ $$24.523$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+(4-\beta _{2})q^{7}+(-\beta _{1}+\beta _{3})q^{11}+(-2+\cdots)q^{13}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$