# Properties

 Label 330.2.w Level $330$ Weight $2$ Character orbit 330.w Rep. character $\chi_{330}(47,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $192$ Newform subspaces $1$ Sturm bound $144$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$330 = 2 \cdot 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 330.w (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$165$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(330, [\chi])$$.

Total New Old
Modular forms 640 192 448
Cusp forms 512 192 320
Eisenstein series 128 0 128

## Trace form

 $$192q + 4q^{3} + 8q^{7} + O(q^{10})$$ $$192q + 4q^{3} + 8q^{7} - 8q^{10} + 16q^{12} - 16q^{13} + 4q^{15} + 48q^{16} - 16q^{21} + 4q^{22} + 48q^{25} + 4q^{27} - 12q^{28} - 16q^{31} - 92q^{33} + 16q^{36} - 40q^{37} - 32q^{42} - 128q^{43} + 32q^{45} - 24q^{46} - 4q^{48} + 88q^{51} - 24q^{52} - 68q^{55} - 48q^{57} - 84q^{58} - 4q^{60} - 48q^{61} - 40q^{63} - 8q^{66} - 208q^{67} - 12q^{70} + 76q^{73} + 92q^{75} - 16q^{78} - 96q^{81} - 16q^{82} - 16q^{85} + 64q^{87} + 4q^{88} + 48q^{90} - 240q^{91} + 28q^{93} + 64q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(330, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
330.2.w.a $$192$$ $$2.635$$ None $$0$$ $$4$$ $$0$$ $$8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(330, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(330, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$