# Properties

 Label 861.2.h Level 861 Weight 2 Character orbit h Rep. character $$\chi_{861}(778,\cdot)$$ Character field $$\Q$$ Dimension 40 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.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$41$$ Character field: $$\Q$$ 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 116 40 76
Cusp forms 108 40 68
Eisenstein series 8 0 8

## Trace form

 $$40q - 4q^{2} + 36q^{4} + 16q^{5} - 12q^{8} - 40q^{9} + O(q^{10})$$ $$40q - 4q^{2} + 36q^{4} + 16q^{5} - 12q^{8} - 40q^{9} - 8q^{10} + 44q^{16} + 4q^{18} + 40q^{20} + 4q^{21} + 24q^{25} - 12q^{31} + 12q^{32} + 12q^{33} - 36q^{36} + 12q^{37} + 16q^{39} + 8q^{40} - 32q^{41} - 4q^{42} + 20q^{43} - 16q^{45} - 40q^{49} - 60q^{50} - 12q^{51} - 16q^{57} + 32q^{59} - 20q^{61} - 24q^{62} + 92q^{64} - 32q^{66} + 12q^{72} + 44q^{73} - 128q^{74} - 40q^{78} + 72q^{80} + 40q^{81} + 16q^{83} + 12q^{84} - 32q^{86} + 28q^{87} + 8q^{90} + 8q^{91} - 128q^{92} + 4q^{98} + O(q^{100})$$

## 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.h.a $$18$$ $$6.875$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+\beta _{5}q^{2}+\beta _{4}q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{14}+\cdots)q^{5}+\cdots$$
861.2.h.b $$22$$ $$6.875$$ None $$-4$$ $$0$$ $$4$$ $$0$$

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

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