Properties

Label 8038.2.a
Level 8038
Weight 2
Character orbit a
Rep. character \(\chi_{8038}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8038))\) into irreducible Hecke orbits

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

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