Space of modular forms of level 1016, weight 1, and Character 1016.h

• Label: 1016.1.h
• Level: $1016$
• Weight: $1$
• Character orbit: 1016.h
• Rep. character: $\chi_{1016}(253,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1016 = 2^{3} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1016.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1016 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1016, [\chi])\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	11	11	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	11	0	0	0

Trace form

\( 11 q - 2 q^{2} + 6 q^{4} - 2 q^{8} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1016, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1016.1.h.a	$1016$	$1$	1016.h	1016.h	$2$	$1$	$1$	$0.507$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-127}) \), \(\Q(\sqrt{-254}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}+2q^{17}+\cdots\)
1016.1.h.b	$1016$	$1$	1016.h	1016.h	$2$	$2$	$2$	$0.507$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-254}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}-\beta q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{8}+\cdots\)
1016.1.h.c	$1016$	$1$	1016.h	1016.h	$2$	$4$	$4$	$0.507$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-254}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1016.1.h.d	$1016$	$1$	1016.h	1016.h	$2$	$4$	$4$	$0.507$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-127}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{8}-q^{9}+\cdots\)