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Properties

Label 6001.2.a
Level $6001$
Weight $2$
Character orbit 6001.a
Rep. character $\chi_{6001}(1,\cdot)$
Character field $\Q$
Dimension $469$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6001))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 17 353
6001.2.a.a 6001.a 1.a $113$ $47.918$ None \(-11\) \(-11\) \(-19\) \(11\) $+$ $+$ $\mathrm{SU}(2)$
6001.2.a.b 6001.a 1.a $114$ $47.918$ None \(-8\) \(-23\) \(-27\) \(-53\) $-$ $-$ $\mathrm{SU}(2)$
6001.2.a.c 6001.a 1.a $121$ $47.918$ None \(9\) \(13\) \(21\) \(-13\) $+$ $-$ $\mathrm{SU}(2)$
6001.2.a.d 6001.a 1.a $121$ $47.918$ None \(9\) \(21\) \(27\) \(39\) $-$ $+$ $\mathrm{SU}(2)$

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

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