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Properties

Label 11.2.a
Level $11$
Weight $2$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(11))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 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.

\(11\)Dim
\(-\)\(1\)

Trace form

\( q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{9} - 2 q^{10} + q^{11} - 2 q^{12} + 4 q^{13} + 4 q^{14} - q^{15} - 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} + 2 q^{21} - 2 q^{22} - q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{27} - 4 q^{28} + 2 q^{30} + 7 q^{31} + 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} - 4 q^{36} + 3 q^{37} - 4 q^{39} - 8 q^{41} - 4 q^{42} - 6 q^{43} + 2 q^{44} - 2 q^{45} + 2 q^{46} + 8 q^{47} + 4 q^{48} - 3 q^{49} + 8 q^{50} + 2 q^{51} + 8 q^{52} - 6 q^{53} - 10 q^{54} + q^{55} + 5 q^{59} - 2 q^{60} + 12 q^{61} - 14 q^{62} + 4 q^{63} - 8 q^{64} + 4 q^{65} + 2 q^{66} - 7 q^{67} - 4 q^{68} + q^{69} + 4 q^{70} - 3 q^{71} + 4 q^{73} - 6 q^{74} + 4 q^{75} - 2 q^{77} + 8 q^{78} - 10 q^{79} - 4 q^{80} + q^{81} + 16 q^{82} - 6 q^{83} + 4 q^{84} - 2 q^{85} + 12 q^{86} + 15 q^{89} + 4 q^{90} - 8 q^{91} - 2 q^{92} - 7 q^{93} - 16 q^{94} - 8 q^{96} - 7 q^{97} + 6 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11
11.2.a.a 11.a 1.a $1$ $0.088$ \(\Q\) None 11.2.a.a \(-2\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)