Properties

Label 8020.2.a
Level $8020$
Weight $2$
Character orbit 8020.a
Rep. character $\chi_{8020}(1,\cdot)$
Character field $\Q$
Dimension $132$
Newform subspaces $6$
Sturm bound $2412$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8020.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(2412\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8020))\).

Total New Old
Modular forms 1212 132 1080
Cusp forms 1201 132 1069
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.

\(2\)\(5\)\(401\)FrickeDim
\(-\)\(+\)\(+\)$-$\(37\)
\(-\)\(+\)\(-\)$+$\(29\)
\(-\)\(-\)\(+\)$+$\(29\)
\(-\)\(-\)\(-\)$-$\(37\)
Plus space\(+\)\(58\)
Minus space\(-\)\(74\)

Trace form

\( 132 q - 4 q^{7} + 128 q^{9} + O(q^{10}) \) \( 132 q - 4 q^{7} + 128 q^{9} + 12 q^{17} - 8 q^{19} + 16 q^{21} - 4 q^{23} + 132 q^{25} - 12 q^{27} - 12 q^{29} + 4 q^{31} + 4 q^{33} - 4 q^{35} - 4 q^{37} + 4 q^{39} - 8 q^{41} + 4 q^{43} - 8 q^{45} - 4 q^{47} + 132 q^{49} + 32 q^{53} + 8 q^{55} - 16 q^{57} - 44 q^{59} - 20 q^{61} + 24 q^{63} + 8 q^{65} - 20 q^{67} + 24 q^{69} + 20 q^{71} - 40 q^{73} - 8 q^{77} - 12 q^{79} + 140 q^{81} - 20 q^{83} - 8 q^{89} - 28 q^{91} - 28 q^{93} - 16 q^{95} - 8 q^{97} - 68 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8020))\) 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 5 401
8020.2.a.a 8020.a 1.a $1$ $64.040$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
8020.2.a.b 8020.a 1.a $2$ $64.040$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
8020.2.a.c 8020.a 1.a $28$ $64.040$ None \(0\) \(3\) \(-28\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$
8020.2.a.d 8020.a 1.a $29$ $64.040$ None \(0\) \(-3\) \(29\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$
8020.2.a.e 8020.a 1.a $35$ $64.040$ None \(0\) \(-1\) \(-35\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$
8020.2.a.f 8020.a 1.a $37$ $64.040$ None \(0\) \(3\) \(37\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(802))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4010))\)\(^{\oplus 2}\)