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Properties

Label 6009.2.a
Level $6009$
Weight $2$
Character orbit 6009.a
Rep. character $\chi_{6009}(1,\cdot)$
Character field $\Q$
Dimension $333$
Newform subspaces $4$
Sturm bound $1336$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 6009 = 3 \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6009.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6009))\).

Total New Old
Modular forms 670 333 337
Cusp forms 667 333 334
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.

\(3\)\(2003\)FrickeDim
\(+\)\(+\)$+$\(74\)
\(+\)\(-\)$-$\(93\)
\(-\)\(+\)$-$\(92\)
\(-\)\(-\)$+$\(74\)
Plus space\(+\)\(148\)
Minus space\(-\)\(185\)

Trace form

\( 333 q + q^{2} - q^{3} + 335 q^{4} - 6 q^{5} + 3 q^{6} + 9 q^{8} + 333 q^{9} + O(q^{10}) \) \( 333 q + q^{2} - q^{3} + 335 q^{4} - 6 q^{5} + 3 q^{6} + 9 q^{8} + 333 q^{9} + 2 q^{10} - 7 q^{12} - 6 q^{13} - 8 q^{14} + 6 q^{15} + 327 q^{16} - 10 q^{17} + q^{18} - 4 q^{19} - 30 q^{20} - 4 q^{21} - 4 q^{22} + 15 q^{24} + 335 q^{25} - 22 q^{26} - q^{27} + 28 q^{28} - 2 q^{29} + 6 q^{30} + 29 q^{32} + 12 q^{33} + 10 q^{34} - 4 q^{35} + 335 q^{36} + 18 q^{37} + 28 q^{38} - 14 q^{39} + 2 q^{40} - 14 q^{41} - 8 q^{43} + 28 q^{44} - 6 q^{45} + 20 q^{46} + 12 q^{47} + q^{48} + 305 q^{49} + 11 q^{50} + 10 q^{51} + 18 q^{52} - 14 q^{53} + 3 q^{54} - 24 q^{55} - 4 q^{56} - 12 q^{57} - 10 q^{58} - 32 q^{59} - 2 q^{60} - 10 q^{61} - 8 q^{62} + 311 q^{64} - 32 q^{65} - 20 q^{66} - 8 q^{67} - 2 q^{68} + 20 q^{69} + 28 q^{70} - 20 q^{71} + 9 q^{72} - 22 q^{73} + 30 q^{74} - 23 q^{75} - 24 q^{76} - 44 q^{77} - 10 q^{78} + 12 q^{79} - 10 q^{80} + 333 q^{81} - 54 q^{82} - 48 q^{83} - 4 q^{84} - 20 q^{85} + 8 q^{86} + 14 q^{87} + 36 q^{88} - 66 q^{89} + 2 q^{90} - 52 q^{91} - 16 q^{92} + 4 q^{93} + 28 q^{94} + 4 q^{95} + 23 q^{96} - 14 q^{97} - 15 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6009))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 2003
6009.2.a.a 6009.a 1.a $74$ $47.982$ None \(-15\) \(74\) \(-34\) \(-24\) $-$ $-$ $\mathrm{SU}(2)$
6009.2.a.b 6009.a 1.a $74$ $47.982$ None \(-3\) \(-74\) \(14\) \(-26\) $+$ $+$ $\mathrm{SU}(2)$
6009.2.a.c 6009.a 1.a $92$ $47.982$ None \(17\) \(92\) \(34\) \(22\) $-$ $+$ $\mathrm{SU}(2)$
6009.2.a.d 6009.a 1.a $93$ $47.982$ None \(2\) \(-93\) \(-20\) \(28\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6009))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2003))\)\(^{\oplus 2}\)