Properties

Label 6001.2.a
Level 6001
Weight 2
Character orbit a
Rep. character \(\chi_{6001}(1,\cdot)\)
Character field \(\Q\)
Dimension 469
Newforms 4
Sturm bound 1062
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1062\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6001))\).

Total New Old
Modular forms 532 469 63
Cusp forms 529 469 60
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.

\(17\)\(353\)FrickeDim.
\(+\)\(+\)\(+\)\(113\)
\(+\)\(-\)\(-\)\(121\)
\(-\)\(+\)\(-\)\(121\)
\(-\)\(-\)\(+\)\(114\)
Plus space\(+\)\(227\)
Minus space\(-\)\(242\)

Trace form

\( 469q - q^{2} + 467q^{4} + 2q^{5} - 16q^{7} - 9q^{8} + 469q^{9} + O(q^{10}) \) \( 469q - q^{2} + 467q^{4} + 2q^{5} - 16q^{7} - 9q^{8} + 469q^{9} - 6q^{10} - 4q^{11} + 16q^{12} - 10q^{13} - 16q^{14} - 4q^{15} + 459q^{16} + q^{17} - 25q^{18} - 12q^{19} - 30q^{20} - 24q^{21} - 16q^{22} - 36q^{24} + 463q^{25} - 18q^{26} + 12q^{27} - 48q^{28} - 22q^{29} - 32q^{30} - 20q^{31} - 29q^{32} + 8q^{33} + 3q^{34} + 4q^{35} + 403q^{36} - 22q^{37} - 28q^{38} + 4q^{39} + 10q^{40} - 14q^{41} + 28q^{42} - 4q^{43} - 20q^{44} + 42q^{45} - 16q^{46} - 4q^{47} + 28q^{48} + 401q^{49} - 39q^{50} - 4q^{51} - 10q^{52} + 14q^{53} - 16q^{54} - 12q^{55} - 144q^{56} - 48q^{57} + 18q^{58} + 12q^{59} - 24q^{60} - 30q^{61} + 16q^{62} - 60q^{63} + 471q^{64} - 20q^{65} - 32q^{66} - 44q^{67} + 7q^{68} + 28q^{69} - 16q^{70} - 8q^{71} - 49q^{72} - 34q^{73} - 30q^{74} - 32q^{75} - 52q^{76} + 16q^{77} + 40q^{78} - 72q^{79} - 42q^{80} + 413q^{81} + 50q^{82} - 24q^{83} + 16q^{84} - 2q^{85} + 28q^{86} - 64q^{87} + 16q^{88} - 26q^{89} + 54q^{90} - 52q^{91} - 64q^{92} + 52q^{93} + 36q^{94} - 48q^{95} - 40q^{96} - 26q^{97} + 59q^{98} - 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6001))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17 353
6001.2.a.a \(113\) \(47.918\) None \(-11\) \(-11\) \(-19\) \(11\) \(+\) \(+\)
6001.2.a.b \(114\) \(47.918\) None \(-8\) \(-23\) \(-27\) \(-53\) \(-\) \(-\)
6001.2.a.c \(121\) \(47.918\) None \(9\) \(13\) \(21\) \(-13\) \(+\) \(-\)
6001.2.a.d \(121\) \(47.918\) None \(9\) \(21\) \(27\) \(39\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6001))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(353))\)\(^{\oplus 2}\)