# Properties

 Label 855.2.k Level $855$ Weight $2$ Character orbit 855.k Rep. character $\chi_{855}(406,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $64$ Newform subspaces $11$ Sturm bound $240$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$855 = 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 855.k (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$11$$ Sturm bound: $$240$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(855, [\chi])$$.

Total New Old
Modular forms 256 64 192
Cusp forms 224 64 160
Eisenstein series 32 0 32

## Trace form

 $$64 q + 2 q^{2} - 30 q^{4} + 4 q^{7} - 12 q^{8} + O(q^{10})$$ $$64 q + 2 q^{2} - 30 q^{4} + 4 q^{7} - 12 q^{8} - 4 q^{10} - 10 q^{13} - 6 q^{14} - 26 q^{16} + 18 q^{17} - 10 q^{19} + 6 q^{22} - 6 q^{23} - 32 q^{25} - 36 q^{26} - 24 q^{28} - 6 q^{29} + 16 q^{31} + 4 q^{32} - 2 q^{34} + 2 q^{35} - 8 q^{37} + 26 q^{38} - 18 q^{40} + 4 q^{41} - 12 q^{43} - 4 q^{44} + 56 q^{46} + 12 q^{47} + 96 q^{49} - 4 q^{50} - 30 q^{52} + 8 q^{53} + 28 q^{56} - 4 q^{58} - 18 q^{59} + 36 q^{61} + 40 q^{62} + 96 q^{64} + 8 q^{65} - 2 q^{67} - 36 q^{68} - 16 q^{70} - 4 q^{71} + 18 q^{73} - 18 q^{74} - 146 q^{76} + 12 q^{77} - 14 q^{79} + 16 q^{80} + 60 q^{82} + 20 q^{83} - 8 q^{85} - 4 q^{86} - 80 q^{88} + 18 q^{89} - 4 q^{91} - 16 q^{92} + 20 q^{94} - 4 q^{95} + 64 q^{97} + 96 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(855, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.2.k.a $2$ $6.827$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-1$$ $$-4$$ $$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
855.2.k.b $2$ $6.827$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-8$$ $$q+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}-4q^{7}-3q^{11}+\cdots$$
855.2.k.c $2$ $6.827$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$4$$ $$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+2q^{7}+3q^{11}+\cdots$$
855.2.k.d $2$ $6.827$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-1$$ $$-4$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
855.2.k.e $4$ $6.827$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$-1$$ $$0$$ $$-2$$ $$12$$ $$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$$
855.2.k.f $4$ $6.827$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$-2$$ $$-4$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$$
855.2.k.g $6$ $6.827$ 6.0.3518667.1 None $$1$$ $$0$$ $$-3$$ $$4$$ $$q+\beta _{1}q^{2}+(-3+\beta _{2}-2\beta _{3}+\beta _{4}-\beta _{5})q^{4}+\cdots$$
855.2.k.h $8$ $6.827$ 8.0.4601315889.1 None $$1$$ $$0$$ $$4$$ $$-8$$ $$q-\beta _{7}q^{2}+(-1+\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7})q^{4}+\cdots$$
855.2.k.i $10$ $6.827$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-1$$ $$0$$ $$5$$ $$4$$ $$q+(\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{3}-\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$$
855.2.k.j $12$ $6.827$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-3$$ $$0$$ $$-6$$ $$4$$ $$q+(\beta _{1}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{9}+\cdots)q^{4}+\cdots$$
855.2.k.k $12$ $6.827$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$3$$ $$0$$ $$6$$ $$4$$ $$q+(-\beta _{1}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(855, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(855, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$