Properties

Label 8012.2.a
Level 8012
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8012))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 2003
8012.2.a.a \(79\) \(63.976\) None \(0\) \(-19\) \(0\) \(-40\) \(-\) \(-\)
8012.2.a.b \(88\) \(63.976\) None \(0\) \(19\) \(0\) \(44\) \(-\) \(+\)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database