Properties

Label 896.1.v
Level $896$
Weight $1$
Character orbit 896.v
Rep. character $\chi_{896}(209,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $4$
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.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
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 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + O(q^{10}) \) \( 4 q + 4 q^{23} + 4 q^{43} - 4 q^{53} - 4 q^{63} - 4 q^{67} - 4 q^{77} + O(q^{100}) \)

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.v.a $4$ $0.447$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(896, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)