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Properties

Label 6007.2.a
Level $6007$
Weight $2$
Character orbit 6007.a
Rep. character $\chi_{6007}(1,\cdot)$
Character field $\Q$
Dimension $500$
Newform subspaces $3$
Sturm bound $1001$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 6007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6007.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1001\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6007))\).

Total New Old
Modular forms 501 501 0
Cusp forms 500 500 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(6007\)Dim
\(+\)\(237\)
\(-\)\(263\)

Trace form

\( 500 q - q^{2} - 2 q^{3} + 499 q^{4} - 6 q^{6} - 6 q^{7} - 3 q^{8} + 500 q^{9} + O(q^{10}) \) \( 500 q - q^{2} - 2 q^{3} + 499 q^{4} - 6 q^{6} - 6 q^{7} - 3 q^{8} + 500 q^{9} - 2 q^{10} - 2 q^{11} - 12 q^{12} + 2 q^{13} + 4 q^{14} - 12 q^{15} + 493 q^{16} + 6 q^{17} - 19 q^{18} + 4 q^{19} - 24 q^{21} - 8 q^{22} - 12 q^{23} - 32 q^{24} + 498 q^{25} - 12 q^{26} - 14 q^{27} - 26 q^{28} + 4 q^{29} - 4 q^{31} + 3 q^{32} - 2 q^{33} + 22 q^{34} - 2 q^{35} + 483 q^{36} - 4 q^{37} - 30 q^{38} - 10 q^{39} + 10 q^{40} + 6 q^{42} - 10 q^{43} - 38 q^{44} - 20 q^{45} + 8 q^{46} + 10 q^{47} - 58 q^{48} + 486 q^{49} - q^{50} + 28 q^{51} + 8 q^{52} - 22 q^{53} - 50 q^{54} - 2 q^{55} - 20 q^{56} - 12 q^{57} - 12 q^{58} + 2 q^{59} - 84 q^{60} + 6 q^{61} - 14 q^{62} - 22 q^{63} + 455 q^{64} - 14 q^{65} - 64 q^{66} + 20 q^{67} - 22 q^{68} - 22 q^{69} - 8 q^{70} + 6 q^{71} - 95 q^{72} - 48 q^{74} - 52 q^{75} + 54 q^{76} - 6 q^{77} - 80 q^{78} - 4 q^{79} - 56 q^{80} + 452 q^{81} + 8 q^{82} + 16 q^{83} - 170 q^{84} + 78 q^{85} - 10 q^{86} - 46 q^{87} - 70 q^{88} - 24 q^{89} - 56 q^{90} - 36 q^{91} - 54 q^{92} - 14 q^{93} - 52 q^{94} - 10 q^{95} - 58 q^{96} - 22 q^{97} - 7 q^{98} - 34 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6007))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 6007
6007.2.a.a 6007.a 1.a $2$ $47.966$ \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(1\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
6007.2.a.b 6007.a 1.a $237$ $47.966$ None \(-26\) \(-24\) \(-67\) \(-37\) $+$ $\mathrm{SU}(2)$
6007.2.a.c 6007.a 1.a $261$ $47.966$ None \(26\) \(25\) \(66\) \(37\) $-$ $\mathrm{SU}(2)$