# Properties

 Label 169.2.e Level $169$ Weight $2$ Character orbit 169.e Rep. character $\chi_{169}(23,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $14$ Newform subspaces $2$ Sturm bound $30$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 169.e (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$30$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 46 34 12
Cusp forms 18 14 4
Eisenstein series 28 20 8

## Trace form

 $$14 q + 3 q^{2} + 2 q^{3} + q^{4} - 6 q^{6} + 5 q^{9} + O(q^{10})$$ $$14 q + 3 q^{2} + 2 q^{3} + q^{4} - 6 q^{6} + 5 q^{9} + 7 q^{10} - 4 q^{12} - 20 q^{14} - 6 q^{15} + q^{16} - q^{17} + 6 q^{19} - 3 q^{20} - 6 q^{22} - 4 q^{23} + 6 q^{24} + 24 q^{25} - 4 q^{27} - q^{29} - 8 q^{30} + 9 q^{32} - 8 q^{35} - 13 q^{36} - 15 q^{37} - 36 q^{38} - 6 q^{40} + 9 q^{41} - 16 q^{42} + 18 q^{43} + 3 q^{45} + 18 q^{46} + 8 q^{48} - 15 q^{49} + 6 q^{50} - 8 q^{51} - 2 q^{53} - 12 q^{54} - 12 q^{55} - 8 q^{56} - 9 q^{58} - 12 q^{59} - 9 q^{61} + 8 q^{62} + 42 q^{64} + 20 q^{66} - 6 q^{67} + 39 q^{68} - 6 q^{71} - 3 q^{72} + q^{74} + 26 q^{75} + 6 q^{76} - 32 q^{77} - 12 q^{79} + 15 q^{80} + 13 q^{81} - 19 q^{82} - 9 q^{85} + 30 q^{87} + 30 q^{88} + 12 q^{89} + 54 q^{90} + 12 q^{92} + 12 q^{93} - 16 q^{94} + 12 q^{95} - 12 q^{97} - 21 q^{98} + O(q^{100})$$

## 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.e.a $2$ $1.349$ $$\Q(\sqrt{-3})$$ None $$3$$ $$-2$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
169.2.e.b $12$ $1.349$ 12.0.$$\cdots$$.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(169, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(169, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 2}$$