Properties

Label 6038.2.a
Level 6038
Weight 2
Character orbit a
Rep. character \(\chi_{6038}(1,\cdot)\)
Character field \(\Q\)
Dimension 252
Newform subspaces 5
Sturm bound 1510
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6038.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1510\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6038))\).

Total New Old
Modular forms 757 252 505
Cusp forms 754 252 502
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.

\(2\)\(3019\)FrickeDim.
\(+\)\(+\)\(+\)\(57\)
\(+\)\(-\)\(-\)\(69\)
\(-\)\(+\)\(-\)\(72\)
\(-\)\(-\)\(+\)\(54\)
Plus space\(+\)\(111\)
Minus space\(-\)\(141\)

Trace form

\( 252q + 4q^{3} + 252q^{4} + 2q^{5} - 2q^{6} + 4q^{7} + 258q^{9} + O(q^{10}) \) \( 252q + 4q^{3} + 252q^{4} + 2q^{5} - 2q^{6} + 4q^{7} + 258q^{9} - 4q^{10} + 12q^{11} + 4q^{12} - 2q^{13} - 4q^{14} - 8q^{15} + 252q^{16} + 12q^{19} + 2q^{20} + 8q^{21} - 6q^{22} + 12q^{23} - 2q^{24} + 254q^{25} + 4q^{26} + 28q^{27} + 4q^{28} + 16q^{29} + 8q^{31} + 4q^{33} - 12q^{34} + 8q^{35} + 258q^{36} + 8q^{37} - 2q^{38} - 8q^{39} - 4q^{40} + 16q^{41} + 8q^{42} + 20q^{43} + 12q^{44} + 10q^{45} - 8q^{46} + 16q^{47} + 4q^{48} + 268q^{49} - 8q^{50} + 28q^{51} - 2q^{52} - 4q^{53} + 4q^{54} + 4q^{55} - 4q^{56} - 4q^{57} - 22q^{58} - 10q^{59} - 8q^{60} - 4q^{61} + 16q^{62} + 252q^{64} + 32q^{65} + 16q^{66} + 8q^{67} + 4q^{69} - 20q^{70} - 12q^{71} + 12q^{73} - 26q^{74} + 56q^{75} + 12q^{76} + 24q^{77} - 8q^{78} + 24q^{79} + 2q^{80} + 260q^{81} - 12q^{82} + 4q^{83} + 8q^{84} - 8q^{85} - 6q^{86} + 4q^{87} - 6q^{88} + 28q^{89} - 16q^{90} + 92q^{91} + 12q^{92} + 32q^{93} - 4q^{94} - 12q^{95} - 2q^{96} + 36q^{97} + 24q^{98} + 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6038))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3019
6038.2.a.a \(2\) \(48.214\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-5\) \(-6\) \(-\) \(+\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots\)
6038.2.a.b \(54\) \(48.214\) None \(54\) \(-21\) \(-14\) \(-44\) \(-\) \(-\)
6038.2.a.c \(57\) \(48.214\) None \(-57\) \(-5\) \(-15\) \(-28\) \(+\) \(+\)
6038.2.a.d \(69\) \(48.214\) None \(-69\) \(8\) \(18\) \(32\) \(+\) \(-\)
6038.2.a.e \(70\) \(48.214\) None \(70\) \(25\) \(18\) \(50\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6038))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3019))\)\(^{\oplus 2}\)