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

• Label: 2156.1.k
• Level: $2156$
• Weight: $1$
• Character orbit: 2156.k
• Rep. character: $\chi_{2156}(373,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $336$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2156.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(336\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	82	16	66
Cusp forms	34	16	18
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - 8 q^{9} + O(q^{10}) \)

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.k.a	$2156$	$1$	2156.k	77.h	$6$	$2$	$1$	$1.076$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None					44.1.d.a	$4$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{11}+q^{15}+\cdots\)
2156.1.k.b	$2156$	$1$	2156.k	77.h	$6$	$2$	$1$	$1.076$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None					44.1.d.a	$4$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{11}+q^{15}+\cdots\)
2156.1.k.c	$2156$	$1$	2156.k	77.h	$6$	$4$	$2$	$1.076$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		✓			2156.1.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
2156.1.k.d	$2156$	$1$	2156.k	77.h	$6$	$8$	$4$	$1.076$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-11}) \)	None		✓	✓		2156.1.h.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$		\(q+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+(\zeta_{24}^{7}+\zeta_{24}^{9}+\cdots)q^{5}+\cdots\)

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

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