# Properties

 Label 845.2.l Level $845$ Weight $2$ Character orbit 845.l Rep. character $\chi_{845}(654,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $136$ Newform subspaces $7$ Sturm bound $182$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$845 = 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 845.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$7$$ Sturm bound: $$182$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(845, [\chi])$$.

Total New Old
Modular forms 208 176 32
Cusp forms 152 136 16
Eisenstein series 56 40 16

## Trace form

 $$136 q - 58 q^{4} + 6 q^{6} + 56 q^{9} + O(q^{10})$$ $$136 q - 58 q^{4} + 6 q^{6} + 56 q^{9} + 8 q^{10} - 60 q^{14} + 6 q^{15} - 26 q^{16} + 12 q^{19} - 24 q^{20} - 12 q^{24} + 4 q^{25} - 4 q^{29} + 44 q^{30} - 10 q^{35} + 16 q^{36} - 20 q^{40} - 12 q^{45} - 42 q^{46} - 20 q^{49} + 12 q^{50} + 16 q^{51} - 30 q^{54} + 22 q^{55} + 60 q^{56} + 60 q^{59} - 28 q^{61} + 8 q^{64} - 20 q^{66} - 12 q^{69} - 12 q^{71} + 50 q^{74} + 14 q^{75} - 6 q^{76} - 96 q^{79} - 18 q^{80} + 36 q^{81} + 6 q^{84} - 42 q^{85} - 48 q^{89} - 116 q^{90} - 72 q^{94} + 20 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(845, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
845.2.l.a $4$ $6.747$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$4$$ $$0$$ $$q+(-1+\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
845.2.l.b $4$ $6.747$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$-4$$ $$0$$ $$q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
845.2.l.c $8$ $6.747$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$$
845.2.l.d $12$ $6.747$ 12.0.$$\cdots$$.1 None $$-6$$ $$0$$ $$4$$ $$4$$ $$q+(-1+\beta _{1}-\beta _{7}+\beta _{10})q^{2}-\beta _{5}q^{3}+\cdots$$
845.2.l.e $12$ $6.747$ 12.0.$$\cdots$$.1 None $$6$$ $$0$$ $$-4$$ $$-4$$ $$q+(1-\beta _{1}+\beta _{7}-\beta _{10})q^{2}+\beta _{5}q^{3}+\cdots$$
845.2.l.f $24$ $6.747$ None $$0$$ $$0$$ $$0$$ $$0$$
845.2.l.g $72$ $6.747$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(845, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(845, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 2}$$