Properties

Label 6002.2.a
Level 6002
Weight 2
Character orbit a
Rep. character \(\chi_{6002}(1,\cdot)\)
Character field \(\Q\)
Dimension 251
Newform subspaces 4
Sturm bound 1501
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 6002 = 2 \cdot 3001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6002.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1501\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6002))\).

Total New Old
Modular forms 752 251 501
Cusp forms 749 251 498
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.

\(2\)\(3001\)FrickeDim.
\(+\)\(+\)\(+\)\(56\)
\(+\)\(-\)\(-\)\(69\)
\(-\)\(+\)\(-\)\(79\)
\(-\)\(-\)\(+\)\(47\)
Plus space\(+\)\(103\)
Minus space\(-\)\(148\)

Trace form

\( 251q + q^{2} + 4q^{3} + 251q^{4} + 2q^{5} + 4q^{6} + 4q^{7} + q^{8} + 255q^{9} + O(q^{10}) \) \( 251q + q^{2} + 4q^{3} + 251q^{4} + 2q^{5} + 4q^{6} + 4q^{7} + q^{8} + 255q^{9} + 6q^{10} - 4q^{11} + 4q^{12} + 8q^{13} + 8q^{15} + 251q^{16} + 2q^{17} + 5q^{18} + 14q^{19} + 2q^{20} + 8q^{21} - 8q^{23} + 4q^{24} + 269q^{25} + 8q^{26} + 4q^{27} + 4q^{28} - 12q^{29} - 16q^{30} + 20q^{31} + q^{32} - 8q^{33} + 18q^{34} - 16q^{35} + 255q^{36} + 14q^{37} - 2q^{38} - 12q^{39} + 6q^{40} + 2q^{41} + 4q^{42} + 10q^{43} - 4q^{44} + 6q^{45} + 4q^{46} - 32q^{47} + 4q^{48} + 259q^{49} + 15q^{50} - 12q^{51} + 8q^{52} + 16q^{53} + 4q^{54} + 12q^{55} - 4q^{57} + 12q^{58} + 12q^{59} + 8q^{60} + 18q^{61} - 8q^{62} + 12q^{63} + 251q^{64} - 8q^{65} + 24q^{66} + 34q^{67} + 2q^{68} + 12q^{69} + 20q^{70} - 4q^{71} + 5q^{72} + 14q^{73} - 2q^{74} + 72q^{75} + 14q^{76} - 12q^{77} - 20q^{78} + 2q^{80} + 283q^{81} + 18q^{82} + 6q^{83} + 8q^{84} + 4q^{85} + 10q^{86} + 12q^{87} + 34q^{89} + 30q^{90} + 40q^{91} - 8q^{92} + 56q^{93} + 8q^{94} + 40q^{95} + 4q^{96} + 62q^{97} + 41q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6002))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3001
6002.2.a.a \(47\) \(47.926\) None \(47\) \(-13\) \(-14\) \(-17\) \(-\) \(-\)
6002.2.a.b \(56\) \(47.926\) None \(-56\) \(-11\) \(0\) \(-21\) \(+\) \(+\)
6002.2.a.c \(69\) \(47.926\) None \(-69\) \(11\) \(-2\) \(23\) \(+\) \(-\)
6002.2.a.d \(79\) \(47.926\) None \(79\) \(17\) \(18\) \(19\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3001))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database