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

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

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

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