Properties

Label 80.2.a
Level $80$
Weight $2$
Character orbit 80.a
Rep. character $\chi_{80}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(80))\).

Total New Old
Modular forms 18 2 16
Cusp forms 7 2 5
Eisenstein series 11 0 11

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.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2 q + 2 q^{3} + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{3} + 2 q^{7} - 2 q^{9} - 4 q^{11} - 2 q^{15} - 4 q^{17} - 4 q^{21} - 10 q^{23} + 2 q^{25} - 4 q^{27} + 4 q^{29} + 12 q^{31} + 6 q^{35} + 8 q^{37} + 4 q^{39} + 18 q^{43} - 4 q^{45} + 2 q^{47} + 6 q^{49} - 12 q^{51} - 4 q^{55} + 8 q^{57} - 8 q^{59} - 14 q^{63} - 4 q^{65} - 10 q^{67} - 12 q^{69} + 12 q^{71} - 4 q^{73} + 2 q^{75} - 16 q^{77} - 8 q^{79} - 2 q^{81} + 10 q^{83} + 8 q^{85} + 12 q^{87} - 12 q^{89} - 12 q^{91} + 8 q^{93} - 8 q^{95} - 12 q^{97} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(80))\) 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
80.2.a.a 80.a 1.a $1$ $0.639$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots\)
80.2.a.b 80.a 1.a $1$ $0.639$ \(\Q\) None \(0\) \(2\) \(-1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(80))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(80)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)