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

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

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

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