Space of modular forms of level 2156, weight 1, and Character 2156.h

• Label: 2156.1.h
• Level: $2156$
• Weight: $1$
• Character orbit: 2156.h
• Rep. character: $\chi_{2156}(197,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $3$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2156.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2156, [\chi])\).

	Total	New	Old
Modular forms	43	7	36
Cusp forms	19	7	12
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	0	0

Trace form

\( 7 q + q^{3} + q^{5} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2156.1.h.a	$2156$	$1$	2156.h	11.b	$2$	$1$	$1$	$1.076$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None	✓				44.1.d.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{3}+q^{5}+q^{11}+q^{15}-q^{23}-q^{27}+\cdots\)
2156.1.h.b	$2156$	$1$	2156.h	11.b	$2$	$2$	$2$	$1.076$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None	✓	✓			2156.1.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{3}+\beta q^{5}+2q^{9}+q^{11}-3q^{15}+\cdots\)
2156.1.h.c	$2156$	$1$	2156.h	11.b	$2$	$4$	$4$	$1.076$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-11}) \)	None	✓	✓	✓		2156.1.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2156, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 3}\)