Properties

Label 8026.2.a
Level 8026
Weight 2
Character orbit a
Rep. character \(\chi_{8026}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8026))\) into irreducible Hecke orbits

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

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