# Properties

 Label 900.3.b Level $900$ Weight $3$ Character orbit 900.b Rep. character $\chi_{900}(449,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $2$ Sturm bound $540$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$540$$ Trace bound: $$1$$ 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

 $$12 q + O(q^{10})$$ $$12 q - 36 q^{19} + 84 q^{31} - 264 q^{49} + 180 q^{61} - 240 q^{79} + 684 q^{91} + O(q^{100})$$

## 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.b.a $4$ $24.523$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}-7\zeta_{8}q^{13}+\zeta_{8}^{3}q^{17}+\cdots$$
900.3.b.b $8$ $24.523$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{1}-\beta _{3})q^{7}+(\beta _{2}+\beta _{5})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$