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Properties

Label 6002.2.a
Level $6002$
Weight $2$
Character orbit 6002.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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6002))\) 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 3001
6002.2.a.a 6002.a 1.a $47$ $47.926$ None \(47\) \(-13\) \(-14\) \(-17\) $-$ $-$ $\mathrm{SU}(2)$
6002.2.a.b 6002.a 1.a $56$ $47.926$ None \(-56\) \(-11\) \(0\) \(-21\) $+$ $+$ $\mathrm{SU}(2)$
6002.2.a.c 6002.a 1.a $69$ $47.926$ None \(-69\) \(11\) \(-2\) \(23\) $+$ $-$ $\mathrm{SU}(2)$
6002.2.a.d 6002.a 1.a $79$ $47.926$ None \(79\) \(17\) \(18\) \(19\) $-$ $+$ $\mathrm{SU}(2)$

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

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