# Properties

 Label 20.2.a Level $20$ Weight $2$ Character orbit 20.a Rep. character $\chi_{20}(1,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 20.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(20))$$.

Total New Old
Modular forms 6 1 5
Cusp forms 1 1 0
Eisenstein series 5 0 5

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

$$2$$$$5$$FrickeDim
$$-$$$$+$$$$-$$$$1$$
Plus space$$+$$$$0$$
Minus space$$-$$$$1$$

## Trace form

 $$q - 2 q^{3} - q^{5} + 2 q^{7} + q^{9} + O(q^{10})$$ $$q - 2 q^{3} - q^{5} + 2 q^{7} + q^{9} + 2 q^{13} + 2 q^{15} - 6 q^{17} - 4 q^{19} - 4 q^{21} + 6 q^{23} + q^{25} + 4 q^{27} + 6 q^{29} - 4 q^{31} - 2 q^{35} + 2 q^{37} - 4 q^{39} + 6 q^{41} - 10 q^{43} - q^{45} - 6 q^{47} - 3 q^{49} + 12 q^{51} - 6 q^{53} + 8 q^{57} + 12 q^{59} + 2 q^{61} + 2 q^{63} - 2 q^{65} + 2 q^{67} - 12 q^{69} - 12 q^{71} + 2 q^{73} - 2 q^{75} + 8 q^{79} - 11 q^{81} + 6 q^{83} + 6 q^{85} - 12 q^{87} - 6 q^{89} + 4 q^{91} + 8 q^{93} + 4 q^{95} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(20))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
20.2.a.a $1$ $0.160$ $$\Q$$ None $$0$$ $$-2$$ $$-1$$ $$2$$ $-$ $+$ $$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$$