Properties

Label 8038.2.a
Level 8038
Weight 2
Character orbit a
Rep. character \(\chi_{8038}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newform subspaces 4
Sturm bound 2010
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 8038 = 2 \cdot 4019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8038.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(2010\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8038))\).

Total New Old
Modular forms 1007 334 673
Cusp forms 1004 334 670
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.

\(2\)\(4019\)FrickeDim.
\(+\)\(+\)\(+\)\(84\)
\(+\)\(-\)\(-\)\(83\)
\(-\)\(+\)\(-\)\(92\)
\(-\)\(-\)\(+\)\(75\)
Plus space\(+\)\(159\)
Minus space\(-\)\(175\)

Trace form

\( 334q + 2q^{3} + 334q^{4} - 2q^{5} - 4q^{7} + 336q^{9} + O(q^{10}) \) \( 334q + 2q^{3} + 334q^{4} - 2q^{5} - 4q^{7} + 336q^{9} + 4q^{11} + 2q^{12} - 4q^{13} + 16q^{15} + 334q^{16} + 4q^{17} - 2q^{19} - 2q^{20} + 10q^{22} - 20q^{23} + 336q^{25} - 2q^{26} - 4q^{27} - 4q^{28} - 12q^{29} - 8q^{31} + 16q^{33} + 4q^{34} + 4q^{35} + 336q^{36} + 4q^{37} + 8q^{38} + 16q^{39} - 4q^{41} - 30q^{43} + 4q^{44} + 22q^{45} + 4q^{46} + 8q^{47} + 2q^{48} + 314q^{49} - 16q^{50} + 16q^{51} - 4q^{52} - 14q^{53} + 12q^{54} + 20q^{55} - 16q^{57} - 6q^{58} + 12q^{59} + 16q^{60} - 28q^{61} - 4q^{62} + 4q^{63} + 334q^{64} + 28q^{65} - 34q^{67} + 4q^{68} + 56q^{69} - 8q^{70} - 4q^{71} - 24q^{73} - 6q^{74} + 46q^{75} - 2q^{76} + 20q^{77} - 44q^{78} + 28q^{79} - 2q^{80} + 374q^{81} - 16q^{82} - 6q^{83} - 40q^{85} + 12q^{86} + 52q^{87} + 10q^{88} + 32q^{89} + 8q^{90} - 20q^{92} + 48q^{93} + 16q^{95} - 24q^{97} + 40q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8038))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4019
8038.2.a.a \(75\) \(64.184\) None \(75\) \(-30\) \(-29\) \(-31\) \(-\) \(-\)
8038.2.a.b \(83\) \(64.184\) None \(-83\) \(20\) \(31\) \(-3\) \(+\) \(-\)
8038.2.a.c \(84\) \(64.184\) None \(-84\) \(-19\) \(-32\) \(1\) \(+\) \(+\)
8038.2.a.d \(92\) \(64.184\) None \(92\) \(31\) \(28\) \(29\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8038))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4019))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database