Properties

Label 896.1.bm
Level $896$
Weight $1$
Character orbit 896.bm
Rep. character $\chi_{896}(13,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $16$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 896.bm (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 896 \)
Character field: \(\Q(\zeta_{32})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(896, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q + O(q^{10}) \) \( 16q - 16q^{56} - 16q^{74} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(896, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
896.1.bm.a \(16\) \(0.447\) \(\Q(\zeta_{32})\) \(D_{32}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{13}q^{2}-\zeta_{32}^{10}q^{4}-\zeta_{32}^{9}q^{7}+\cdots\)