Properties

Label 6007.2.a
Level 6007
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6007
6007.2.a.a \(2\) \(47.966\) \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(1\) \(-6\) \(-\) \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
6007.2.a.b \(237\) \(47.966\) None \(-26\) \(-24\) \(-67\) \(-37\) \(+\)
6007.2.a.c \(261\) \(47.966\) None \(26\) \(25\) \(66\) \(37\) \(-\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))
$3$ (\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))
$5$ (\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))
$7$ (\( ( 1 + 3 T + 7 T^{2} )^{2} \))
$11$ (\( 1 - 4 T + 21 T^{2} - 44 T^{3} + 121 T^{4} \))
$13$ (\( ( 1 + 3 T + 13 T^{2} )^{2} \))
$17$ (\( 1 + 9 T + 53 T^{2} + 153 T^{3} + 289 T^{4} \))
$19$ (\( ( 1 + 3 T + 19 T^{2} )^{2} \))
$23$ (\( 1 + 10 T + 66 T^{2} + 230 T^{3} + 529 T^{4} \))
$29$ (\( 1 + 8 T + 54 T^{2} + 232 T^{3} + 841 T^{4} \))
$31$ (\( 1 + 9 T + 71 T^{2} + 279 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 9 T + 83 T^{2} - 333 T^{3} + 1369 T^{4} \))
$41$ (\( ( 1 + 6 T + 41 T^{2} )^{2} \))
$43$ (\( 1 + 11 T + 85 T^{2} + 473 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 6 T + 83 T^{2} + 282 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 5 T + 111 T^{2} - 265 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + T + 87 T^{2} + 59 T^{3} + 3481 T^{4} \))
$61$ (\( 1 + 10 T + 142 T^{2} + 610 T^{3} + 3721 T^{4} \))
$67$ (\( ( 1 - 3 T + 67 T^{2} )^{2} \))
$71$ (\( 1 + 29 T + 351 T^{2} + 2059 T^{3} + 5041 T^{4} \))
$73$ (\( ( 1 + 73 T^{2} )^{2} \))
$79$ (\( 1 + T + 97 T^{2} + 79 T^{3} + 6241 T^{4} \))
$83$ (\( 1 + 4 T + 45 T^{2} + 332 T^{3} + 6889 T^{4} \))
$89$ (\( 1 - 8 T + 174 T^{2} - 712 T^{3} + 7921 T^{4} \))
$97$ (\( 1 + 14 T + 223 T^{2} + 1358 T^{3} + 9409 T^{4} \))
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