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 $0$

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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 Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
20.2.a.a 20.a 1.a $1$ $0.160$ \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)