# Properties

 Label 770.2.bm Level $770$ Weight $2$ Character orbit 770.bm Rep. character $\chi_{770}(61,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $256$ Newform subspaces $2$ Sturm bound $288$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$770 = 2 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 770.bm (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$6$$ 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 256 960
Cusp forms 1088 256 832
Eisenstein series 128 0 128

## Trace form

 $$256q - 32q^{4} - 44q^{9} + O(q^{10})$$ $$256q - 32q^{4} - 44q^{9} + 6q^{11} - 2q^{14} + 24q^{15} + 32q^{16} + 60q^{17} + 8q^{22} + 24q^{23} - 32q^{25} + 60q^{26} - 40q^{29} + 24q^{33} - 48q^{36} + 8q^{37} + 24q^{38} - 20q^{39} - 40q^{42} - 6q^{44} + 24q^{47} + 60q^{49} + 60q^{51} + 24q^{53} + 8q^{58} + 120q^{59} - 8q^{60} - 200q^{63} + 64q^{64} + 48q^{66} - 32q^{67} - 60q^{68} + 128q^{71} - 40q^{72} - 180q^{73} - 40q^{74} - 60q^{77} - 192q^{78} - 60q^{79} + 60q^{81} - 72q^{82} - 80q^{84} + 16q^{86} - 16q^{88} - 48q^{89} - 98q^{91} - 72q^{92} - 100q^{93} + 90q^{94} - 116q^{99} + O(q^{100})$$

## 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.bm.a $$128$$ $$6.148$$ None $$0$$ $$0$$ $$0$$ $$0$$
770.2.bm.b $$128$$ $$6.148$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(770, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(385, [\chi])$$$$^{\oplus 2}$$