# Properties

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

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 26.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$7$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(26))$$.

Total New Old
Modular forms 5 2 3
Cusp forms 2 2 0
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$$$13$$FrickeDim
$$+$$$$-$$$$-$$$$1$$
$$-$$$$+$$$$-$$$$1$$
Plus space$$+$$$$0$$
Minus space$$-$$$$2$$

## Trace form

 $$2 q - 2 q^{3} + 2 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{9} + O(q^{10})$$ $$2 q - 2 q^{3} + 2 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{14} + 2 q^{16} - 6 q^{17} + 8 q^{18} + 8 q^{19} - 4 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{23} - 4 q^{24} - 2 q^{26} - 14 q^{27} + 8 q^{29} + 6 q^{30} + 12 q^{33} + 2 q^{35} + 4 q^{36} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 2 q^{40} - 2 q^{42} - 6 q^{43} + 4 q^{44} - 4 q^{46} + 16 q^{47} - 2 q^{48} - 12 q^{49} - 8 q^{50} + 6 q^{51} + 12 q^{53} - 4 q^{54} - 16 q^{55} + 2 q^{56} - 16 q^{57} - 4 q^{58} - 16 q^{59} + 8 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 12 q^{67} - 6 q^{68} + 12 q^{69} - 4 q^{70} - 8 q^{71} + 8 q^{72} - 8 q^{73} + 10 q^{74} + 16 q^{75} + 8 q^{76} - 8 q^{77} + 2 q^{78} + 4 q^{79} - 4 q^{80} + 10 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 4 q^{86} - 8 q^{88} - 12 q^{90} - 2 q^{91} - 4 q^{92} - 16 q^{93} + 10 q^{94} - 12 q^{95} - 4 q^{96} + 4 q^{97} - 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(26))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 13
26.2.a.a $1$ $0.208$ $$\Q$$ None $$-1$$ $$1$$ $$-3$$ $$-1$$ $+$ $-$ $$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$$
26.2.a.b $1$ $0.208$ $$\Q$$ None $$1$$ $$-3$$ $$-1$$ $$1$$ $-$ $+$ $$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$$