# Properties

 Label 833.2.b Level $833$ Weight $2$ Character orbit 833.b Rep. character $\chi_{833}(50,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $5$ Sturm bound $168$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$833 = 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 833.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$168$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$2$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(833, [\chi])$$.

Total New Old
Modular forms 92 66 26
Cusp forms 76 56 20
Eisenstein series 16 10 6

## Trace form

 $$56 q + 4 q^{2} + 56 q^{4} - 52 q^{9} + O(q^{10})$$ $$56 q + 4 q^{2} + 56 q^{4} - 52 q^{9} + 8 q^{13} + 40 q^{16} - 2 q^{17} - 36 q^{18} - 4 q^{19} - 48 q^{25} - 12 q^{26} + 28 q^{30} - 16 q^{32} + 20 q^{33} - 6 q^{34} - 84 q^{36} + 4 q^{38} - 20 q^{43} + 32 q^{50} + 28 q^{51} + 64 q^{52} - 40 q^{53} + 12 q^{55} - 56 q^{59} + 68 q^{60} + 12 q^{64} - 72 q^{66} - 24 q^{67} + 22 q^{68} - 28 q^{69} - 40 q^{72} + 12 q^{76} + 8 q^{81} + 12 q^{83} + 48 q^{85} + 92 q^{86} + 52 q^{87} + 4 q^{89} + 36 q^{93} + 20 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(833, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
833.2.b.a $10$ $6.652$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{1}-\beta _{2})q^{4}+\cdots$$
833.2.b.b $10$ $6.652$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ $$\Q(\sqrt{-119})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{8})q^{4}-\beta _{5}q^{5}+\cdots$$
833.2.b.c $10$ $6.652$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots$$
833.2.b.d $10$ $6.652$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots$$
833.2.b.e $16$ $6.652$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}-\beta _{1}q^{3}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(833, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(833, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(119, [\chi])$$$$^{\oplus 2}$$