# Properties

 Label 20.6.a Level $20$ Weight $6$ Character orbit 20.a Rep. character $\chi_{20}(1,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 20.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_0(20))$$.

Total New Old
Modular forms 18 1 17
Cusp forms 12 1 11
Eisenstein series 6 0 6

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

 $$q + 22 q^{3} - 25 q^{5} + 218 q^{7} + 241 q^{9} + O(q^{10})$$ $$q + 22 q^{3} - 25 q^{5} + 218 q^{7} + 241 q^{9} - 480 q^{11} - 622 q^{13} - 550 q^{15} + 186 q^{17} - 1204 q^{19} + 4796 q^{21} - 3186 q^{23} + 625 q^{25} - 44 q^{27} + 5526 q^{29} + 9356 q^{31} - 10560 q^{33} - 5450 q^{35} + 5618 q^{37} - 13684 q^{39} - 14394 q^{41} - 370 q^{43} - 6025 q^{45} + 16146 q^{47} + 30717 q^{49} + 4092 q^{51} - 4374 q^{53} + 12000 q^{55} - 26488 q^{57} - 11748 q^{59} + 13202 q^{61} + 52538 q^{63} + 15550 q^{65} - 11542 q^{67} - 70092 q^{69} - 29532 q^{71} + 33698 q^{73} + 13750 q^{75} - 104640 q^{77} + 31208 q^{79} - 59531 q^{81} - 38466 q^{83} - 4650 q^{85} + 121572 q^{87} + 119514 q^{89} - 135596 q^{91} + 205832 q^{93} + 30100 q^{95} + 94658 q^{97} - 115680 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_0(20))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
20.6.a.a $1$ $3.208$ $$\Q$$ None $$0$$ $$22$$ $$-25$$ $$218$$ $-$ $+$ $$q+22q^{3}-5^{2}q^{5}+218q^{7}+241q^{9}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_0(20))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_0(20)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_0(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_0(5))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_0(10))$$$$^{\oplus 2}$$