Properties

Label 8026.2.a
Level 8026
Weight 2
Character orbit a
Rep. character \(\chi_{8026}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newform subspaces 4
Sturm bound 2007
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8026.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(2007\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8026))\).

Total New Old
Modular forms 1005 334 671
Cusp forms 1002 334 668
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.

\(2\)\(4013\)FrickeDim.
\(+\)\(+\)\(+\)\(81\)
\(+\)\(-\)\(-\)\(86\)
\(-\)\(+\)\(-\)\(96\)
\(-\)\(-\)\(+\)\(71\)
Plus space\(+\)\(152\)
Minus space\(-\)\(182\)

Trace form

\( 334q + 334q^{4} + 4q^{5} - 2q^{6} + 328q^{9} + O(q^{10}) \) \( 334q + 334q^{4} + 4q^{5} - 2q^{6} + 328q^{9} + 6q^{10} + 2q^{11} - 2q^{13} + 334q^{16} + 16q^{17} - 10q^{19} + 4q^{20} - 4q^{22} + 12q^{23} - 2q^{24} + 340q^{25} + 4q^{26} - 24q^{30} - 4q^{31} - 20q^{33} - 8q^{34} + 4q^{35} + 328q^{36} - 4q^{37} - 16q^{38} - 56q^{39} + 6q^{40} + 12q^{41} - 6q^{43} + 2q^{44} + 20q^{45} - 8q^{46} + 16q^{47} + 346q^{49} + 8q^{50} - 16q^{51} - 2q^{52} + 10q^{53} - 20q^{54} + 32q^{55} - 20q^{57} + 10q^{58} - 6q^{59} - 22q^{61} + 8q^{62} - 44q^{63} + 334q^{64} - 4q^{65} - 16q^{66} - 14q^{67} + 16q^{68} - 28q^{69} + 20q^{70} + 4q^{73} + 10q^{74} - 28q^{75} - 10q^{76} + 16q^{77} + 20q^{78} - 20q^{79} + 4q^{80} + 294q^{81} + 16q^{82} - 2q^{83} - 4q^{85} - 8q^{86} - 4q^{87} - 4q^{88} + 4q^{89} + 30q^{90} + 4q^{91} + 12q^{92} + 8q^{93} + 4q^{94} - 28q^{95} - 2q^{96} - 4q^{97} + 46q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8026))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4013
8026.2.a.a \(71\) \(64.088\) None \(71\) \(-9\) \(-34\) \(-19\) \(-\) \(-\)
8026.2.a.b \(81\) \(64.088\) None \(-81\) \(-10\) \(-26\) \(3\) \(+\) \(+\)
8026.2.a.c \(86\) \(64.088\) None \(-86\) \(11\) \(25\) \(-3\) \(+\) \(-\)
8026.2.a.d \(96\) \(64.088\) None \(96\) \(8\) \(39\) \(19\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4013))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database