Properties

Label 2011.2.a
Level 2011
Weight 2
Character orbit a
Rep. character \(\chi_{2011}(1,\cdot)\)
Character field \(\Q\)
Dimension 167
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\) into newform subspaces

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 \(11\) \(9\) \(47\) \(4\) \(-\)