# Properties

 Label 770.2.bc Level $770$ Weight $2$ Character orbit 770.bc Rep. character $\chi_{770}(243,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $160$ Newform subspaces $2$ Sturm bound $288$ Trace bound $11$

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## Defining parameters

 Level: $$N$$ $$=$$ $$770 = 2 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 770.bc (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(770, [\chi])$$.

Total New Old
Modular forms 608 160 448
Cusp forms 544 160 384
Eisenstein series 64 0 64

## Trace form

 $$160q + O(q^{10})$$ $$160q - 48q^{15} + 80q^{16} + 72q^{17} + 16q^{18} + 56q^{21} - 24q^{30} - 48q^{31} + 24q^{35} - 144q^{36} - 48q^{38} - 48q^{42} - 64q^{43} - 72q^{45} + 24q^{46} + 16q^{53} - 8q^{56} + 80q^{57} + 32q^{58} - 16q^{60} + 24q^{61} + 136q^{63} - 16q^{65} - 16q^{67} + 72q^{68} - 16q^{70} - 64q^{71} + 16q^{72} - 96q^{73} - 48q^{75} - 32q^{78} + 64q^{81} + 48q^{82} - 96q^{85} - 24q^{86} + 72q^{87} + 64q^{91} - 8q^{93} - 16q^{95} - 24q^{96} - 112q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(770, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
770.2.bc.a $$80$$ $$6.148$$ None $$0$$ $$0$$ $$0$$ $$0$$
770.2.bc.b $$80$$ $$6.148$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(770, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(770, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(385, [\chi])$$$$^{\oplus 2}$$