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Properties

Label 11.3.b
Level $11$
Weight $3$
Character orbit 11.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.3.b.a 11.b 11.b $1$ $0.300$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-5\) \(-1\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots\)