Properties

Label 6017.2.a
Level 6017
Weight 2
Character orbit a
Rep. character \(\chi_{6017}(1,\cdot)\)
Character field \(\Q\)
Dimension 455
Newform subspaces 6
Sturm bound 1096
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1096\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6017))\).

Total New Old
Modular forms 550 455 95
Cusp forms 547 455 92
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.

\(11\)\(547\)FrickeDim.
\(+\)\(+\)\(+\)\(107\)
\(+\)\(-\)\(-\)\(122\)
\(-\)\(+\)\(-\)\(120\)
\(-\)\(-\)\(+\)\(106\)
Plus space\(+\)\(213\)
Minus space\(-\)\(242\)

Trace form

\( 455q + q^{2} + 2q^{3} + 451q^{4} - 4q^{5} + 4q^{6} + 8q^{7} + 9q^{8} + 461q^{9} + O(q^{10}) \) \( 455q + q^{2} + 2q^{3} + 451q^{4} - 4q^{5} + 4q^{6} + 8q^{7} + 9q^{8} + 461q^{9} - 2q^{10} - 3q^{11} - 2q^{13} - 4q^{14} - 10q^{15} + 455q^{16} - 2q^{17} - 7q^{18} + 14q^{20} + 32q^{21} + 3q^{22} + 2q^{23} + 16q^{24} + 451q^{25} + 30q^{26} + 26q^{27} + 24q^{28} + 2q^{29} - 16q^{30} + 2q^{31} - 11q^{32} + 2q^{33} - 46q^{34} + 24q^{35} + 431q^{36} - 4q^{37} + 24q^{38} + 24q^{39} - 26q^{40} - 6q^{41} + 16q^{42} + 28q^{43} - 3q^{44} - 26q^{45} + 32q^{46} - 4q^{47} - 40q^{48} + 495q^{49} - 97q^{50} - 20q^{51} + 18q^{52} - 2q^{53} - 8q^{54} - 12q^{57} + 6q^{58} + 14q^{59} - 48q^{60} - 10q^{61} + 12q^{62} + 48q^{63} + 439q^{64} - 48q^{65} - 16q^{66} + 30q^{67} - 22q^{68} - 30q^{69} - 12q^{70} + 38q^{71} - 19q^{72} - 10q^{73} - 26q^{74} + 68q^{75} + 20q^{76} + 8q^{77} - 140q^{78} + 40q^{79} - 42q^{80} + 479q^{81} + 6q^{82} - 4q^{83} + 40q^{84} - 52q^{85} + 4q^{86} + 36q^{87} - 9q^{88} - 4q^{89} - 10q^{90} + 64q^{91} - 96q^{92} + 98q^{93} - 44q^{94} + 20q^{95} + 48q^{96} - 75q^{98} - 9q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 547
6017.2.a.a \(1\) \(48.046\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(q-2q^{4}-2q^{7}-3q^{9}-q^{11}-5q^{13}+\cdots\)
6017.2.a.b \(1\) \(48.046\) \(\Q\) None \(0\) \(2\) \(4\) \(2\) \(-\) \(+\) \(q+2q^{3}-2q^{4}+4q^{5}+2q^{7}+q^{9}+\cdots\)
6017.2.a.c \(106\) \(48.046\) None \(-13\) \(-15\) \(-12\) \(-66\) \(-\) \(-\)
6017.2.a.d \(107\) \(48.046\) None \(-3\) \(-18\) \(-15\) \(-54\) \(+\) \(+\)
6017.2.a.e \(119\) \(48.046\) None \(15\) \(15\) \(6\) \(72\) \(-\) \(+\)
6017.2.a.f \(121\) \(48.046\) None \(2\) \(18\) \(13\) \(56\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(547))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))
$3$ (\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))
$11$ (\( 1 + T \))(\( 1 - T \))
$13$ (\( 1 + 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))
$29$ (\( 1 + T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))
$47$ (\( 1 + 9 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))
$61$ (\( 1 + 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))
$67$ (\( 1 + 5 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))
$73$ (\( 1 + 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))
$79$ (\( 1 + 6 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))
$89$ (\( 1 - 8 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))
$97$ (\( 1 - 15 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))
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