Properties

Label 11.3.b
Level 11
Weight 3
Character orbit b
Rep. character \(\chi_{11}(10,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 11.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(11, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 5q^{3} + 4q^{4} - q^{5} + 16q^{9} + O(q^{10}) \) \( q - 5q^{3} + 4q^{4} - q^{5} + 16q^{9} - 11q^{11} - 20q^{12} + 5q^{15} + 16q^{16} - 4q^{20} + 35q^{23} - 24q^{25} - 35q^{27} - 37q^{31} + 55q^{33} + 64q^{36} - 25q^{37} - 44q^{44} - 16q^{45} + 50q^{47} - 80q^{48} + 49q^{49} - 70q^{53} + 11q^{55} + 107q^{59} + 20q^{60} + 64q^{64} + 35q^{67} - 175q^{69} - 133q^{71} + 120q^{75} - 16q^{80} + 31q^{81} - 97q^{89} + 140q^{92} + 185q^{93} + 95q^{97} - 176q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.3.b.a \(1\) \(0.300\) \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-5\) \(-1\) \(0\) \(q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 2 T )( 1 + 2 T ) \)
$3$ \( 1 + 5 T + 9 T^{2} \)
$5$ \( 1 + T + 25 T^{2} \)
$7$ \( ( 1 - 7 T )( 1 + 7 T ) \)
$11$ \( 1 + 11 T \)
$13$ \( ( 1 - 13 T )( 1 + 13 T ) \)
$17$ \( ( 1 - 17 T )( 1 + 17 T ) \)
$19$ \( ( 1 - 19 T )( 1 + 19 T ) \)
$23$ \( 1 - 35 T + 529 T^{2} \)
$29$ \( ( 1 - 29 T )( 1 + 29 T ) \)
$31$ \( 1 + 37 T + 961 T^{2} \)
$37$ \( 1 + 25 T + 1369 T^{2} \)
$41$ \( ( 1 - 41 T )( 1 + 41 T ) \)
$43$ \( ( 1 - 43 T )( 1 + 43 T ) \)
$47$ \( 1 - 50 T + 2209 T^{2} \)
$53$ \( 1 + 70 T + 2809 T^{2} \)
$59$ \( 1 - 107 T + 3481 T^{2} \)
$61$ \( ( 1 - 61 T )( 1 + 61 T ) \)
$67$ \( 1 - 35 T + 4489 T^{2} \)
$71$ \( 1 + 133 T + 5041 T^{2} \)
$73$ \( ( 1 - 73 T )( 1 + 73 T ) \)
$79$ \( ( 1 - 79 T )( 1 + 79 T ) \)
$83$ \( ( 1 - 83 T )( 1 + 83 T ) \)
$89$ \( 1 + 97 T + 7921 T^{2} \)
$97$ \( 1 - 95 T + 9409 T^{2} \)
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