# Properties

 Label 900.3.u Level $900$ Weight $3$ Character orbit 900.u Rep. character $\chi_{900}(149,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $4$ Sturm bound $540$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.u (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$540$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 756 72 684
Cusp forms 684 72 612
Eisenstein series 72 0 72

## Trace form

 $$72q - 14q^{9} + O(q^{10})$$ $$72q - 14q^{9} + 36q^{11} - 8q^{21} - 72q^{29} - 30q^{31} + 8q^{39} + 72q^{41} + 204q^{49} - 198q^{51} - 18q^{59} - 96q^{61} + 396q^{69} - 108q^{79} + 158q^{81} + 168q^{91} - 606q^{99} + O(q^{100})$$

## 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.u.a $$8$$ $$24.523$$ 8.0.303595776.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(-3\beta _{1}-3\beta _{4}+\cdots)q^{7}+\cdots$$
900.3.u.b $$8$$ $$24.523$$ 8.0.12960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\beta _{1}q^{3}+(4\beta _{1}+\beta _{6})q^{7}-9\beta _{2}q^{9}+\cdots$$
900.3.u.c $$24$$ $$24.523$$ None $$0$$ $$0$$ $$0$$ $$0$$
900.3.u.d $$32$$ $$24.523$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$