Properties

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

Related objects

Downloads

Learn more about

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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(11, [\chi])\) into irreducible Hecke orbits

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