# Properties

 Label 26.2.b Level $26$ Weight $2$ Character orbit 26.b Rep. character $\chi_{26}(25,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $7$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 26.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(26, [\chi])$$.

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

## Trace form

 $$2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} + O(q^{10})$$ $$2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 6 q^{14} + 2 q^{16} + 6 q^{17} - 12 q^{23} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 6 q^{30} + 18 q^{35} + 4 q^{36} + 12 q^{38} - 4 q^{39} - 6 q^{40} + 6 q^{42} - 2 q^{43} - 2 q^{48} - 4 q^{49} - 6 q^{51} - 4 q^{52} - 12 q^{53} + 6 q^{56} - 16 q^{61} - 2 q^{64} + 18 q^{65} - 6 q^{68} + 12 q^{69} - 6 q^{74} + 8 q^{75} + 6 q^{78} + 20 q^{79} + 2 q^{81} - 12 q^{90} - 18 q^{91} + 12 q^{92} - 6 q^{94} - 36 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(26, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.2.b.a $2$ $0.208$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots$$