Properties

Label 896.1.h
Level $896$
Weight $1$
Character orbit 896.h
Rep. character $\chi_{896}(321,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $128$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 896.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 28 4 24
Cusp forms 12 4 8
Eisenstein series 16 0 16

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

\( 4 q + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{9} + 4 q^{25} + 4 q^{49} - 8 q^{57} - 8 q^{65} - 4 q^{81} + O(q^{100}) \)

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.h.a \(2\) \(0.447\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{3}-\beta q^{5}-q^{7}+q^{9}+\beta q^{13}+\cdots\)
896.1.h.b \(2\) \(0.447\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{3}-\beta q^{5}+q^{7}+q^{9}+\beta q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)