Properties

Label 111.1.d
Level $111$
Weight $1$
Character orbit 111.d
Rep. character $\chi_{111}(110,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 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

\( 3 q - q^{3} + q^{4} - 2 q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q - q^{3} + q^{4} - 2 q^{7} + 3 q^{9} - 4 q^{10} - 3 q^{12} - q^{16} - 2 q^{21} + q^{25} - q^{27} + 2 q^{28} + 4 q^{30} + 4 q^{34} + q^{36} - q^{37} - 4 q^{46} + 3 q^{48} + q^{49} + 4 q^{58} - 2 q^{63} - 3 q^{64} - 2 q^{67} - 2 q^{73} - 3 q^{75} + 3 q^{81} + 2 q^{84} - 4 q^{85} - 4 q^{90} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
111.1.d.a 111.d 111.d $1$ $0.055$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(1\) \(0\) \(-2\) \(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
111.1.d.b 111.d 111.d $2$ $0.055$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-111}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)