Properties

Label 6017.2.a
Level 6017
Weight 2
Character orbit a
Rep. character \(\chi_{6017}(1,\cdot)\)
Character field \(\Q\)
Dimension 455
Newforms 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: \(\Q\)
Newforms: \( 6 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\) into irreducible Hecke orbits

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

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