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Properties

Label 6011.2.a
Level $6011$
Weight $2$
Character orbit 6011.a
Rep. character $\chi_{6011}(1,\cdot)$
Character field $\Q$
Dimension $501$
Newform subspaces $6$
Sturm bound $1002$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 6011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6011.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1002\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6011))\).

Total New Old
Modular forms 502 502 0
Cusp forms 501 501 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.

\(6011\)Dim
\(+\)\(224\)
\(-\)\(277\)

Trace form

\( 501 q - 2 q^{3} + 504 q^{4} - 4 q^{6} - 6 q^{8} + 501 q^{9} + O(q^{10}) \) \( 501 q - 2 q^{3} + 504 q^{4} - 4 q^{6} - 6 q^{8} + 501 q^{9} - 8 q^{10} - 2 q^{11} - 22 q^{12} + 6 q^{13} - 18 q^{14} - 10 q^{15} + 506 q^{16} - 10 q^{18} - 2 q^{20} + 16 q^{21} - 4 q^{22} - 6 q^{23} - 22 q^{24} + 497 q^{25} - 6 q^{26} - 8 q^{27} - 12 q^{28} + 4 q^{29} - 34 q^{30} + 2 q^{31} - 22 q^{32} - 28 q^{33} - 20 q^{34} - 4 q^{35} + 502 q^{36} + 14 q^{37} + 16 q^{38} - 2 q^{39} - 24 q^{40} - 10 q^{41} - 14 q^{42} - 8 q^{43} + 2 q^{45} + 6 q^{46} - 54 q^{48} + 491 q^{49} + 10 q^{50} - 12 q^{51} - 22 q^{52} - 18 q^{53} - 26 q^{54} - 56 q^{55} - 14 q^{56} - 12 q^{57} - 44 q^{58} - 22 q^{59} - 74 q^{60} + 18 q^{61} - 2 q^{62} + 10 q^{63} + 490 q^{64} - 24 q^{65} - 56 q^{66} + 6 q^{67} - 32 q^{68} - 50 q^{69} - 82 q^{70} + 10 q^{71} - 72 q^{72} - 6 q^{73} + 48 q^{74} + 56 q^{75} - 14 q^{76} - 26 q^{77} - 22 q^{78} + 26 q^{79} + 4 q^{80} + 477 q^{81} + 18 q^{82} + 24 q^{83} + 104 q^{84} + 24 q^{85} - 22 q^{86} + 34 q^{87} - 36 q^{88} + 18 q^{89} - 22 q^{90} - 6 q^{91} + 74 q^{92} - 38 q^{93} - 12 q^{94} - 28 q^{95} - 26 q^{96} + 4 q^{97} + 26 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6011))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 6011
6011.2.a.a 6011.a 1.a $1$ $47.998$ \(\Q\) None \(-2\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}+q^{7}-3q^{9}+\cdots\)
6011.2.a.b 6011.a 1.a $1$ $47.998$ \(\Q\) None \(0\) \(3\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{4}+q^{5}-q^{7}+6q^{9}+6q^{11}+\cdots\)
6011.2.a.c 6011.a 1.a $1$ $47.998$ \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
6011.2.a.d 6011.a 1.a $2$ $47.998$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+2q^{3}+2\beta q^{5}+2\beta q^{6}-q^{7}+\cdots\)
6011.2.a.e 6011.a 1.a $221$ $47.998$ None \(-15\) \(-17\) \(-32\) \(-40\) $+$ $\mathrm{SU}(2)$
6011.2.a.f 6011.a 1.a $275$ $47.998$ None \(16\) \(9\) \(36\) \(41\) $-$ $\mathrm{SU}(2)$