# Properties

 Label 290.2.b Level $290$ Weight $2$ Character orbit 290.b Rep. character $\chi_{290}(59,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $2$ Sturm bound $90$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$290 = 2 \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 290.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$90$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(290, [\chi])$$.

Total New Old
Modular forms 50 14 36
Cusp forms 42 14 28
Eisenstein series 8 0 8

## Trace form

 $$14 q - 14 q^{4} - 22 q^{9} + O(q^{10})$$ $$14 q - 14 q^{4} - 22 q^{9} + 8 q^{11} - 4 q^{14} + 8 q^{15} + 14 q^{16} + 16 q^{19} - 8 q^{21} - 24 q^{25} + 8 q^{26} - 6 q^{29} - 6 q^{30} + 8 q^{31} + 8 q^{35} + 22 q^{36} - 24 q^{39} - 4 q^{41} - 8 q^{44} + 26 q^{45} + 20 q^{46} - 18 q^{49} - 16 q^{50} - 32 q^{51} + 12 q^{54} + 16 q^{55} + 4 q^{56} + 20 q^{59} - 8 q^{60} - 20 q^{61} - 14 q^{64} + 10 q^{65} + 24 q^{66} - 8 q^{69} - 20 q^{70} - 8 q^{71} + 12 q^{74} + 20 q^{75} - 16 q^{76} + 48 q^{79} - 2 q^{81} + 8 q^{84} + 28 q^{85} - 16 q^{86} - 28 q^{89} - 4 q^{90} - 40 q^{91} - 4 q^{94} - 8 q^{95} + 64 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(290, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
290.2.b.a $4$ $2.316$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$$
290.2.b.b $10$ $2.316$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{5})q^{3}-q^{4}+\beta _{3}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(290, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(290, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 2}$$