Properties

Label 56.1.h
Level $56$
Weight $1$
Character orbit 56.h
Rep. character $\chi_{56}(13,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 56.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(56, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 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 1 0 0 0

Trace form

\( q - q^{2} + q^{4} - q^{7} - q^{8} - q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} - q^{9} + q^{14} + q^{16} + q^{18} + 2q^{23} - q^{25} - q^{28} - q^{32} - q^{36} - 2q^{46} + q^{49} + q^{50} + q^{56} + q^{63} + q^{64} - 2q^{71} + q^{72} - 2q^{79} + q^{81} + 2q^{92} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(56, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
56.1.h.a \(1\) \(0.028\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\)