Properties

Label 20.4.a
Level $20$
Weight $4$
Character orbit 20.a
Rep. character $\chi_{20}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 20.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(20))\).

Total New Old
Modular forms 12 1 11
Cusp forms 6 1 5
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\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\( q + 4 q^{3} + 5 q^{5} - 16 q^{7} - 11 q^{9} + O(q^{10}) \) \( q + 4 q^{3} + 5 q^{5} - 16 q^{7} - 11 q^{9} - 60 q^{11} + 86 q^{13} + 20 q^{15} + 18 q^{17} + 44 q^{19} - 64 q^{21} + 48 q^{23} + 25 q^{25} - 152 q^{27} - 186 q^{29} + 176 q^{31} - 240 q^{33} - 80 q^{35} + 254 q^{37} + 344 q^{39} + 186 q^{41} - 100 q^{43} - 55 q^{45} + 168 q^{47} - 87 q^{49} + 72 q^{51} - 498 q^{53} - 300 q^{55} + 176 q^{57} - 252 q^{59} - 58 q^{61} + 176 q^{63} + 430 q^{65} - 1036 q^{67} + 192 q^{69} + 168 q^{71} + 506 q^{73} + 100 q^{75} + 960 q^{77} + 272 q^{79} - 311 q^{81} + 948 q^{83} + 90 q^{85} - 744 q^{87} - 1014 q^{89} - 1376 q^{91} + 704 q^{93} + 220 q^{95} - 766 q^{97} + 660 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(20))\) 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
20.4.a.a 20.a 1.a $1$ $1.180$ \(\Q\) None \(0\) \(4\) \(5\) \(-16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

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