Properties

Label 6017.2.a
Level $6017$
Weight $2$
Character orbit 6017.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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 547
6017.2.a.a 6017.a 1.a $1$ $48.046$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{7}-3q^{9}-q^{11}-5q^{13}+\cdots\)
6017.2.a.b 6017.a 1.a $1$ $48.046$ \(\Q\) None \(0\) \(2\) \(4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+4q^{5}+2q^{7}+q^{9}+\cdots\)
6017.2.a.c 6017.a 1.a $106$ $48.046$ None \(-13\) \(-15\) \(-12\) \(-66\) $-$ $-$ $\mathrm{SU}(2)$
6017.2.a.d 6017.a 1.a $107$ $48.046$ None \(-3\) \(-18\) \(-15\) \(-54\) $+$ $+$ $\mathrm{SU}(2)$
6017.2.a.e 6017.a 1.a $119$ $48.046$ None \(15\) \(15\) \(6\) \(72\) $-$ $+$ $\mathrm{SU}(2)$
6017.2.a.f 6017.a 1.a $121$ $48.046$ None \(2\) \(18\) \(13\) \(56\) $+$ $-$ $\mathrm{SU}(2)$

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

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