Properties

Label 8006.2.a
Level 8006
Weight 2
Character orbit a
Rep. character \(\chi_{8006}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8006))\) into newform subspaces

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database