Properties

Label 6011.2.a
Level 6011
Weight 2
Character orbit a
Rep. character \(\chi_{6011}(1,\cdot)\)
Character field \(\Q\)
Dimension 501
Newforms 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: \(\Q\)
Newforms: \( 6 \)
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.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6011))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6011
6011.2.a.a \(1\) \(47.998\) \(\Q\) None \(-2\) \(0\) \(-2\) \(1\) \(-\) \(q-2q^{2}+2q^{4}-2q^{5}+q^{7}-3q^{9}+\cdots\)
6011.2.a.b \(1\) \(47.998\) \(\Q\) None \(0\) \(3\) \(1\) \(-1\) \(-\) \(q+3q^{3}-2q^{4}+q^{5}-q^{7}+6q^{9}+6q^{11}+\cdots\)
6011.2.a.c \(1\) \(47.998\) \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) \(+\) \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
6011.2.a.d \(2\) \(47.998\) \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(0\) \(-2\) \(+\) \(q+\beta q^{2}+2q^{3}+2\beta q^{5}+2\beta q^{6}-q^{7}+\cdots\)
6011.2.a.e \(221\) \(47.998\) None \(-15\) \(-17\) \(-32\) \(-40\) \(+\)
6011.2.a.f \(275\) \(47.998\) None \(16\) \(9\) \(36\) \(41\) \(-\)