Properties

Label 8044.2.a
Level 8044
Weight 2
Character orbit a
Rep. character \(\chi_{8044}(1,\cdot)\)
Character field \(\Q\)
Dimension 167
Newforms 2
Sturm bound 2012
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8044 = 2^{2} \cdot 2011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8044.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(2012\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8044))\).

Total New Old
Modular forms 1009 167 842
Cusp forms 1004 167 837
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.

\(2\)\(2011\)FrickeDim.
\(-\)\(+\)\(-\)\(87\)
\(-\)\(-\)\(+\)\(80\)
Plus space\(+\)\(80\)
Minus space\(-\)\(87\)

Trace form

\( 167q - 4q^{5} - 4q^{7} + 161q^{9} + O(q^{10}) \) \( 167q - 4q^{5} - 4q^{7} + 161q^{9} + 2q^{11} - 2q^{13} - 8q^{15} - 4q^{17} + 4q^{19} - 6q^{21} - 4q^{23} + 151q^{25} + 6q^{27} - 10q^{29} - 10q^{31} + 2q^{33} - 4q^{35} - 22q^{37} - 20q^{39} + 2q^{41} - 6q^{43} - 28q^{45} - 16q^{47} + 143q^{49} + 18q^{51} + 6q^{53} - 18q^{55} - 20q^{57} + 6q^{59} - 26q^{61} - 22q^{63} - 14q^{65} + 10q^{67} - 20q^{69} + 14q^{71} + 2q^{73} + 12q^{75} + 8q^{77} - 36q^{79} + 143q^{81} - 16q^{83} - 4q^{85} + 2q^{87} - 4q^{89} + 26q^{91} + 36q^{95} + 2q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8044))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 2011
8044.2.a.a \(80\) \(64.232\) None \(0\) \(-13\) \(-2\) \(-12\) \(-\) \(-\)
8044.2.a.b \(87\) \(64.232\) None \(0\) \(13\) \(-2\) \(8\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8044))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4022))\)\(^{\oplus 2}\)