Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 8012 = 2^{2} \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8012.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8012))\) into irreducible Hecke orbits

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

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