# Properties

 Label 169.2.c Level $169$ Weight $2$ Character orbit 169.c Rep. character $\chi_{169}(22,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $3$ Sturm bound $30$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 169.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$30$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(169, [\chi])$$.

Total New Old
Modular forms 44 36 8
Cusp forms 16 16 0
Eisenstein series 28 20 8

## Trace form

 $$16 q - 2 q^{4} + 4 q^{9} + O(q^{10})$$ $$16 q - 2 q^{4} + 4 q^{9} - 4 q^{10} + 8 q^{12} - 20 q^{14} + 6 q^{16} - 2 q^{17} - 6 q^{22} - 2 q^{23} - 28 q^{25} - 12 q^{27} - 4 q^{29} + 14 q^{30} - 8 q^{35} + 12 q^{36} + 24 q^{38} - 16 q^{42} - 10 q^{43} + 18 q^{48} + 22 q^{49} + 20 q^{51} - 8 q^{53} - 12 q^{55} + 8 q^{56} - 10 q^{61} - 14 q^{62} - 40 q^{64} + 20 q^{66} + 36 q^{68} - 12 q^{69} - 14 q^{74} - 22 q^{75} + 32 q^{77} - 4 q^{79} + 24 q^{81} + 10 q^{82} + 24 q^{87} - 30 q^{88} - 60 q^{90} + 24 q^{92} - 22 q^{94} - 18 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(169, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
169.2.c.a $4$ $1.349$ $$\Q(\zeta_{12})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}-2\zeta_{12}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots$$
169.2.c.b $6$ $1.349$ 6.0.64827.1 None $$-2$$ $$2$$ $$8$$ $$-3$$ $$q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots$$
169.2.c.c $6$ $1.349$ 6.0.64827.1 None $$2$$ $$2$$ $$-8$$ $$3$$ $$q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$$