# Properties

 Label 861.2.bo Level 861 Weight 2 Character orbit bo Rep. character $$\chi_{861}(43,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 352 Newforms 2 Sturm bound 224 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$861 = 3 \cdot 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 861.bo (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$41$$ Character field: $$\Q(\zeta_{20})$$ Newforms: $$2$$ Sturm bound: $$224$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(861, [\chi])$$.

Total New Old
Modular forms 928 352 576
Cusp forms 864 352 512
Eisenstein series 64 0 64

## Trace form

 $$352q + 96q^{4} + O(q^{10})$$ $$352q + 96q^{4} + 48q^{10} - 8q^{11} + 16q^{12} + 8q^{13} + 32q^{15} - 112q^{16} + 16q^{17} - 8q^{19} - 8q^{22} + 24q^{23} + 56q^{25} - 16q^{26} + 24q^{30} - 32q^{31} - 24q^{34} + 8q^{35} - 8q^{37} + 96q^{38} + 64q^{40} - 8q^{41} + 32q^{42} - 8q^{44} + 16q^{45} - 80q^{46} + 88q^{47} - 32q^{48} - 24q^{51} - 104q^{52} - 40q^{53} + 136q^{55} + 8q^{57} + 8q^{58} + 32q^{60} + 144q^{64} + 192q^{65} - 80q^{66} + 24q^{67} - 64q^{68} + 40q^{69} - 8q^{70} - 136q^{71} + 80q^{74} + 48q^{75} - 72q^{76} - 136q^{78} - 32q^{79} - 400q^{80} - 352q^{81} + 184q^{82} + 32q^{85} - 192q^{86} - 80q^{87} + 24q^{88} - 40q^{89} - 240q^{92} - 72q^{93} - 64q^{94} - 80q^{95} - 40q^{96} + 112q^{97} + 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(861, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
861.2.bo.a $$160$$ $$6.875$$ None $$0$$ $$0$$ $$0$$ $$0$$
861.2.bo.b $$192$$ $$6.875$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(861, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(861, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(41, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(123, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 2}$$