Properties

Label 8012.2.a
Level $8012$
Weight $2$
Character orbit 8012.a
Rep. character $\chi_{8012}(1,\cdot)$
Character field $\Q$
Dimension $167$
Newform subspaces $2$
Sturm bound $2004$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8012 = 2^{2} \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8012.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(2004\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8012))\).

Total New Old
Modular forms 1005 167 838
Cusp forms 1000 167 833
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.

\(2\)\(2003\)FrickeDim
\(-\)\(+\)$-$\(88\)
\(-\)\(-\)$+$\(79\)
Plus space\(+\)\(79\)
Minus space\(-\)\(88\)

Trace form

\( 167 q + 4 q^{7} + 171 q^{9} + O(q^{10}) \) \( 167 q + 4 q^{7} + 171 q^{9} + 2 q^{11} - 6 q^{13} + 2 q^{15} + 2 q^{17} + 14 q^{21} - 16 q^{23} + 165 q^{25} + 12 q^{27} + 4 q^{29} - 8 q^{31} + 6 q^{33} - 8 q^{35} + 2 q^{39} + 2 q^{41} - 6 q^{43} + 24 q^{45} + 10 q^{47} + 183 q^{49} + 14 q^{51} - 2 q^{53} + 4 q^{55} + 28 q^{57} + 10 q^{59} + 12 q^{63} + 18 q^{65} + 8 q^{67} + 30 q^{69} - 4 q^{71} + 16 q^{73} - 16 q^{75} + 8 q^{77} + 12 q^{79} + 175 q^{81} - 6 q^{83} + 14 q^{85} + 6 q^{87} - 36 q^{89} - 10 q^{91} - 14 q^{93} - 10 q^{95} + 24 q^{97} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8012))\) 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 2003
8012.2.a.a 8012.a 1.a $79$ $63.976$ None \(0\) \(-19\) \(0\) \(-40\) $-$ $-$ $\mathrm{SU}(2)$
8012.2.a.b 8012.a 1.a $88$ $63.976$ None \(0\) \(19\) \(0\) \(44\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4006))\)\(^{\oplus 2}\)