Properties

Label 112.1.l
Level $112$
Weight $1$
Character orbit 112.l
Rep. character $\chi_{112}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 112.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(112, [\chi])\).

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

\( 2q - 2q^{4} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{11} - 2q^{14} + 2q^{16} + 2q^{18} + 2q^{22} - 2q^{29} - 2q^{37} + 2q^{43} + 2q^{44} - 2q^{49} - 2q^{50} + 2q^{53} + 2q^{56} - 2q^{58} + 2q^{63} - 2q^{64} + 2q^{67} - 2q^{72} + 2q^{74} + 2q^{77} - 2q^{81} - 2q^{86} - 2q^{88} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
112.1.l.a \(2\) \(0.056\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots\)