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

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

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

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