Properties

Label 8042.2.a
Level 8042
Weight 2
Character orbit a
Rep. character \(\chi_{8042}(1,\cdot)\)
Character field \(\Q\)
Dimension 336
Newforms 4
Sturm bound 2011
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(2011\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8042))\).

Total New Old
Modular forms 1007 336 671
Cusp forms 1004 336 668
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.

\(2\)\(4021\)FrickeDim.
\(+\)\(+\)\(+\)\(82\)
\(+\)\(-\)\(-\)\(86\)
\(-\)\(+\)\(-\)\(101\)
\(-\)\(-\)\(+\)\(67\)
Plus space\(+\)\(149\)
Minus space\(-\)\(187\)

Trace form

\( 336q - 2q^{3} + 336q^{4} - 2q^{5} + 334q^{9} + O(q^{10}) \) \( 336q - 2q^{3} + 336q^{4} - 2q^{5} + 334q^{9} - 12q^{11} - 2q^{12} + 10q^{13} + 4q^{14} + 4q^{15} + 336q^{16} + 8q^{17} + 8q^{18} + 8q^{19} - 2q^{20} + 20q^{21} - 6q^{22} + 4q^{23} + 330q^{25} + 4q^{26} + 4q^{27} - 12q^{30} - 12q^{31} + 12q^{33} - 8q^{34} - 4q^{35} + 334q^{36} + 2q^{37} - 2q^{38} + 16q^{39} - 4q^{41} - 8q^{42} - 12q^{43} - 12q^{44} - 6q^{45} + 4q^{46} + 24q^{47} - 2q^{48} + 340q^{49} + 4q^{51} + 10q^{52} + 14q^{53} - 4q^{55} + 4q^{56} + 28q^{57} - 2q^{58} - 46q^{59} + 4q^{60} + 30q^{61} + 20q^{62} + 48q^{63} + 336q^{64} + 16q^{65} + 22q^{67} + 8q^{68} + 20q^{69} - 4q^{70} + 8q^{71} + 8q^{72} + 24q^{74} + 18q^{75} + 8q^{76} - 16q^{77} + 4q^{78} - 8q^{79} - 2q^{80} + 320q^{81} + 12q^{82} + 2q^{83} + 20q^{84} - 20q^{85} + 30q^{86} - 12q^{87} - 6q^{88} + 16q^{89} + 4q^{90} + 36q^{91} + 4q^{92} + 20q^{93} - 12q^{94} - 20q^{95} - 12q^{97} + 40q^{98} - 132q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8042))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4021
8042.2.a.a \(67\) \(64.216\) None \(67\) \(-11\) \(-20\) \(-40\) \(-\) \(-\)
8042.2.a.b \(82\) \(64.216\) None \(-82\) \(-13\) \(3\) \(-37\) \(+\) \(+\)
8042.2.a.c \(86\) \(64.216\) None \(-86\) \(12\) \(-4\) \(35\) \(+\) \(-\)
8042.2.a.d \(101\) \(64.216\) None \(101\) \(10\) \(19\) \(42\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4021))\)\(^{\oplus 2}\)