Properties

Label 11.2.a
Level 11
Weight 2
Character orbit 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.

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

Trace form

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.2.a.a \(1\) \(0.088\) \(\Q\) None \(-2\) \(-1\) \(1\) \(-2\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 2 T^{2} \)
$3$ \( 1 + T + 3 T^{2} \)
$5$ \( 1 - T + 5 T^{2} \)
$7$ \( 1 + 2 T + 7 T^{2} \)
$11$ \( 1 - T \)
$13$ \( 1 - 4 T + 13 T^{2} \)
$17$ \( 1 + 2 T + 17 T^{2} \)
$19$ \( 1 + 19 T^{2} \)
$23$ \( 1 + T + 23 T^{2} \)
$29$ \( 1 + 29 T^{2} \)
$31$ \( 1 - 7 T + 31 T^{2} \)
$37$ \( 1 - 3 T + 37 T^{2} \)
$41$ \( 1 + 8 T + 41 T^{2} \)
$43$ \( 1 + 6 T + 43 T^{2} \)
$47$ \( 1 - 8 T + 47 T^{2} \)
$53$ \( 1 + 6 T + 53 T^{2} \)
$59$ \( 1 - 5 T + 59 T^{2} \)
$61$ \( 1 - 12 T + 61 T^{2} \)
$67$ \( 1 + 7 T + 67 T^{2} \)
$71$ \( 1 + 3 T + 71 T^{2} \)
$73$ \( 1 - 4 T + 73 T^{2} \)
$79$ \( 1 + 10 T + 79 T^{2} \)
$83$ \( 1 + 6 T + 83 T^{2} \)
$89$ \( 1 - 15 T + 89 T^{2} \)
$97$ \( 1 + 7 T + 97 T^{2} \)
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