Properties

Label 8006.2.a
Level 8006
Weight 2
Character orbit a
Rep. character \(\chi_{8006}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newforms 4
Sturm bound 2002
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8006.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(2002\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8006))\).

Total New Old
Modular forms 1003 334 669
Cusp forms 1000 334 666
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(4003\)FrickeDim.
\(+\)\(+\)\(+\)\(75\)
\(+\)\(-\)\(-\)\(92\)
\(-\)\(+\)\(-\)\(98\)
\(-\)\(-\)\(+\)\(69\)
Plus space\(+\)\(144\)
Minus space\(-\)\(190\)

Trace form

\(334q \) \(\mathstrut +\mathstrut 334q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 340q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(334q \) \(\mathstrut +\mathstrut 334q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 340q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 334q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 328q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 340q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 32q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 322q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 46q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut -\mathstrut 32q^{55} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 10q^{59} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 36q^{63} \) \(\mathstrut +\mathstrut 334q^{64} \) \(\mathstrut -\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 12q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 28q^{78} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 342q^{81} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 84q^{93} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 56q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 32q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8006))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4003
8006.2.a.a \(69\) \(63.928\) None \(69\) \(-15\) \(-9\) \(-29\) \(-\) \(-\)
8006.2.a.b \(75\) \(63.928\) None \(-75\) \(1\) \(-9\) \(-8\) \(+\) \(+\)
8006.2.a.c \(92\) \(63.928\) None \(-92\) \(-2\) \(10\) \(8\) \(+\) \(-\)
8006.2.a.d \(98\) \(63.928\) None \(98\) \(16\) \(4\) \(29\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4003))\)\(^{\oplus 2}\)