Space of modular forms of level 896, weight 1, and Character 896.h

• 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: $7$

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

\( 4 q + 4 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
896.1.h.a	$896$	$1$	896.h	56.h	$2$	$2$	$2$	$0.447$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\beta q^{3}-\beta q^{5}-q^{7}+q^{9}+\beta q^{13}+\cdots\)
896.1.h.b	$896$	$1$	896.h	56.h	$2$	$2$	$2$	$0.447$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\beta q^{3}-\beta q^{5}+q^{7}+q^{9}+\beta q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)