Properties

Label 2011.2.a
Level 2011
Weight 2
Character orbit a
Rep. character \(\chi_{2011}(1,\cdot)\)
Character field \(\Q\)
Dimension 167
Newforms 2
Sturm bound 335
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2011.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(335\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2011))\).

Total New Old
Modular forms 168 168 0
Cusp forms 167 167 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.

\(2011\)Dim.
\(+\)\(77\)
\(-\)\(90\)

Trace form

\(167q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 162q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 161q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(167q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 162q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 161q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 140q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 175q^{25} \) \(\mathstrut -\mathstrut 16q^{26} \) \(\mathstrut -\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 8q^{32} \) \(\mathstrut -\mathstrut 22q^{33} \) \(\mathstrut +\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 122q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 28q^{43} \) \(\mathstrut -\mathstrut 52q^{44} \) \(\mathstrut -\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 34q^{48} \) \(\mathstrut +\mathstrut 159q^{49} \) \(\mathstrut +\mathstrut 38q^{50} \) \(\mathstrut -\mathstrut 42q^{51} \) \(\mathstrut +\mathstrut 48q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 12q^{54} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 16q^{56} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 54q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 108q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 12q^{68} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 22q^{72} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 44q^{75} \) \(\mathstrut -\mathstrut 54q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 14q^{80} \) \(\mathstrut +\mathstrut 191q^{81} \) \(\mathstrut +\mathstrut 14q^{82} \) \(\mathstrut -\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 42q^{84} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 34q^{86} \) \(\mathstrut +\mathstrut 42q^{87} \) \(\mathstrut -\mathstrut 76q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 62q^{91} \) \(\mathstrut -\mathstrut 32q^{92} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut -\mathstrut 14q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 42q^{98} \) \(\mathstrut -\mathstrut 76q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2011
2011.2.a.a \(77\) \(16.058\) None \(-13\) \(-13\) \(-47\) \(-8\) \(+\)
2011.2.a.b \(90\) \(16.058\) None \(11\) \(9\) \(47\) \(4\) \(-\)