# Properties

 Label 770.2.bh Level $770$ Weight $2$ Character orbit 770.bh Rep. character $\chi_{770}(57,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $288$ Newform subspaces $2$ Sturm bound $288$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$770 = 2 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 770.bh (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{20})$$ 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 1216 288 928
Cusp forms 1088 288 800
Eisenstein series 128 0 128

## Trace form

 $$288q + 8q^{3} + O(q^{10})$$ $$288q + 8q^{3} - 8q^{11} + 32q^{12} + 8q^{15} + 72q^{16} + 8q^{20} + 8q^{22} + 32q^{23} - 16q^{27} - 32q^{31} + 40q^{33} + 88q^{36} - 8q^{37} + 72q^{38} - 96q^{45} - 80q^{46} - 24q^{47} - 8q^{48} - 80q^{50} + 40q^{51} - 80q^{52} - 80q^{53} - 160q^{55} - 160q^{57} - 40q^{60} - 80q^{62} - 48q^{66} - 160q^{67} + 16q^{70} + 96q^{71} - 72q^{75} + 16q^{77} - 32q^{78} + 160q^{81} - 32q^{82} + 80q^{85} + 112q^{86} + 8q^{88} + 72q^{91} + 8q^{92} - 112q^{93} - 80q^{95} - 88q^{97} + O(q^{100})$$

## 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.bh.a $$144$$ $$6.148$$ None $$0$$ $$4$$ $$0$$ $$0$$
770.2.bh.b $$144$$ $$6.148$$ None $$0$$ $$4$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(770, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(385, [\chi])$$$$^{\oplus 2}$$