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Properties

Label 8038.2.a
Level $8038$
Weight $2$
Character orbit 8038.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 4019
8038.2.a.a 8038.a 1.a $75$ $64.184$ None \(75\) \(-30\) \(-29\) \(-31\) $-$ $-$ $\mathrm{SU}(2)$
8038.2.a.b 8038.a 1.a $83$ $64.184$ None \(-83\) \(20\) \(31\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$
8038.2.a.c 8038.a 1.a $84$ $64.184$ None \(-84\) \(-19\) \(-32\) \(1\) $+$ $+$ $\mathrm{SU}(2)$
8038.2.a.d 8038.a 1.a $92$ $64.184$ None \(92\) \(31\) \(28\) \(29\) $-$ $+$ $\mathrm{SU}(2)$

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

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