Properties

Label 20.8.a
Level $20$
Weight $8$
Character orbit 20.a
Rep. character $\chi_{20}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 20.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(20))\).

Total New Old
Modular forms 24 3 21
Cusp forms 18 3 15
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
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\( 3 q - 26 q^{3} + 125 q^{5} + 954 q^{7} + 2707 q^{9} + O(q^{10}) \) \( 3 q - 26 q^{3} + 125 q^{5} + 954 q^{7} + 2707 q^{9} - 240 q^{11} + 9126 q^{13} - 1750 q^{15} + 6318 q^{17} - 19428 q^{19} - 93652 q^{21} + 43518 q^{23} + 46875 q^{25} - 159452 q^{27} + 35562 q^{29} - 261492 q^{31} + 799920 q^{33} + 295750 q^{35} - 191946 q^{37} - 432628 q^{39} - 1042662 q^{41} + 2083230 q^{43} + 876125 q^{45} - 1832862 q^{47} + 137199 q^{49} - 4286724 q^{51} + 3235902 q^{53} + 930000 q^{55} - 1347304 q^{57} - 1362996 q^{59} - 4346634 q^{61} + 7176506 q^{63} + 2154250 q^{65} + 290634 q^{67} - 662844 q^{69} - 805116 q^{71} + 3433686 q^{73} - 406250 q^{75} - 1616880 q^{77} + 5934696 q^{79} - 229433 q^{81} - 5962722 q^{83} + 575250 q^{85} - 3939564 q^{87} - 9031362 q^{89} + 16727892 q^{91} - 26418136 q^{93} - 7689500 q^{95} + 18000534 q^{97} + 746640 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(20))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
20.8.a.a 20.a 1.a $1$ $6.248$ \(\Q\) None \(0\) \(-6\) \(-125\) \(-706\) $-$ $+$ $\mathrm{SU}(2)$ \(q-6q^{3}-5^{3}q^{5}-706q^{7}-2151q^{9}+\cdots\)
20.8.a.b 20.a 1.a $2$ $6.248$ \(\Q(\sqrt{1129}) \) None \(0\) \(-20\) \(250\) \(1660\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-10-\beta )q^{3}+5^{3}q^{5}+(830+9\beta )q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)