# Properties

 Label 300.2.w Level $300$ Weight $2$ Character orbit 300.w Rep. character $\chi_{300}(67,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $240$ Newform subspaces $1$ Sturm bound $120$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 300.w (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$100$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$120$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(300, [\chi])$$.

Total New Old
Modular forms 512 240 272
Cusp forms 448 240 208
Eisenstein series 64 0 64

## Trace form

 $$240q + 12q^{8} + O(q^{10})$$ $$240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(300, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
300.2.w.a $$240$$ $$2.396$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(300, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(300, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$