# Properties

 Label 540.3.b Level $540$ Weight $3$ Character orbit 540.b Rep. character $\chi_{540}(269,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $3$ Sturm bound $324$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$540 = 2^{2} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 540.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$324$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(540, [\chi])$$.

Total New Old
Modular forms 234 16 218
Cusp forms 198 16 182
Eisenstein series 36 0 36

## Trace form

 $$16 q + O(q^{10})$$ $$16 q - 24 q^{19} + 30 q^{25} + 76 q^{31} + 48 q^{49} + 134 q^{55} - 40 q^{61} + 300 q^{79} - 40 q^{85} + 204 q^{91} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(540, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
540.3.b.a $4$ $14.714$ $$\Q(\sqrt{-11}, \sqrt{-19})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{11}+\cdots$$
540.3.b.b $4$ $14.714$ $$\Q(\sqrt{-11}, \sqrt{-19})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(1+\beta _{3})q^{5}-\beta _{2}q^{7}+(2\beta _{1}+3\beta _{2}+\cdots)q^{11}+\cdots$$
540.3.b.c $8$ $14.714$ 8.0.$$\cdots$$.13 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-\beta _{6}q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(540, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(540, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 2}$$