Properties

Label 111.1.h
Level $111$
Weight $1$
Character orbit 111.h
Rep. character $\chi_{111}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(111, [\chi])\) into newform subspaces

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