Properties

Label 111.1.i
Level 111
Weight 1
Character orbit i
Rep. character \(\chi_{111}(26,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 111 = 3 \cdot 37 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 111.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 111 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(111, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{3} - q^{4} + q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - q^{4} + q^{7} - q^{9} - q^{12} + q^{13} - q^{16} - 2q^{19} + q^{21} - q^{25} + 2q^{27} + q^{28} - 2q^{31} + 2q^{36} + 2q^{37} + q^{39} - 2q^{43} + 2q^{48} + q^{52} - 2q^{57} - 2q^{61} - 2q^{63} + 2q^{64} + q^{67} - 2q^{73} + 2q^{75} - 2q^{76} + q^{79} - q^{81} - 2q^{84} - q^{91} + q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(111, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
111.1.i.a \(2\) \(0.055\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)