Properties

Label 6002.2.a
Level 6002
Weight 2
Character orbit a
Rep. character \(\chi_{6002}(1,\cdot)\)
Character field \(\Q\)
Dimension 251
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6002))\) into irreducible Hecke orbits

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

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