Space of modular forms of level 2696, weight 1, and Character 2696.h

• Label: 2696.1.h
• Level: $2696$
• Weight: $1$
• Character orbit: 2696.h
• Rep. character: $\chi_{2696}(1347,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $6$
• Sturm bound: $338$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2696 = 2^{3} \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2696.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2696 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(338\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2696, [\chi])\).

	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

\( 11 q - q^{2} - 2 q^{3} + 11 q^{4} - 2 q^{6} - q^{8} + 9 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2696, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2696.1.h.a	$2696$	$1$	2696.h	2696.h	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-674}) \)	\(\Q(\sqrt{337}) \)	✓	$4$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+3q^{9}+\cdots\)
2696.1.h.b	$2696$	$1$	2696.h	2696.h	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-674}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(-2\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
2696.1.h.c	$2696$	$1$	2696.h	2696.h	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-674}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(2\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
2696.1.h.d	$2696$	$1$	2696.h	2696.h	$2$	$2$	$2$	$1.345$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-674}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}-q^{9}+\beta q^{10}+\cdots\)
2696.1.h.e	$2696$	$1$	2696.h	2696.h	$2$	$2$	$2$	$1.345$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-674}) \)	None	✓	$4$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{12}+\cdots\)
2696.1.h.f	$2696$	$1$	2696.h	2696.h	$2$	$4$	$4$	$1.345$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-674}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)