Properties

Label 2011.1.b
Level 2011
Weight 1
Character orbit b
Rep. character \(\chi_{2011}(2010,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 1
Sturm bound 167
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2011 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2011.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2011 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(167\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2011, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\(3q \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut q^{43} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2011, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2011.1.b.a \(3\) \(1.004\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-2011}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)