# Properties

 Label 119.2.b Level $119$ Weight $2$ Character orbit 119.b Rep. character $\chi_{119}(50,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$119 = 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 119.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(119, [\chi])$$.

Total New Old
Modular forms 14 10 4
Cusp forms 10 10 0
Eisenstein series 4 0 4

## Trace form

 $$10 q - 4 q^{2} + 4 q^{4} - 12 q^{8} - 6 q^{9} + O(q^{10})$$ $$10 q - 4 q^{2} + 4 q^{4} - 12 q^{8} - 6 q^{9} - 8 q^{13} - 8 q^{15} + 8 q^{16} + 2 q^{17} + 12 q^{18} + 4 q^{19} - 2 q^{25} + 12 q^{26} + 10 q^{30} - 18 q^{32} - 20 q^{33} + 6 q^{34} + 8 q^{35} + 10 q^{36} - 4 q^{38} - 14 q^{42} + 16 q^{43} - 10 q^{49} + 6 q^{50} - 64 q^{52} + 8 q^{53} - 12 q^{55} + 56 q^{59} - 26 q^{60} + 72 q^{66} + 24 q^{67} - 22 q^{68} + 28 q^{69} + 4 q^{70} + 10 q^{72} - 12 q^{76} + 2 q^{81} - 12 q^{83} + 24 q^{84} - 20 q^{85} - 74 q^{86} - 52 q^{87} - 4 q^{89} + 32 q^{93} - 20 q^{94} + 4 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(119, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
119.2.b.a $10$ $0.950$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$