Space of modular forms of level 2156, weight 2, and Character 2156.c

• Label: 2156.2.c
• Level: $2156$
• Weight: $2$
• Character orbit: 2156.c
• Rep. character: $\chi_{2156}(1077,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $672$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2156.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(672\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2156, [\chi])\).

	Total	New	Old
Modular forms	360	40	320
Cusp forms	312	40	272
Eisenstein series	48	0	48

Trace form

\( 40 q - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2156.2.c.a	$2156$	$2$	2156.c	77.b	$2$	$8$	$8$	$17.216$	8.0.\(\cdots\).1	None		✓			2156.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
2156.2.c.b	$2156$	$2$	2156.c	77.b	$2$	$16$	$16$	$17.216$	16.0.\(\cdots\).1	\(\Q(\sqrt{-11}) \)		✓			2156.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 7^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{3}+\beta _{11}q^{5}+(-3+\beta _{6})q^{9}+\cdots\)
2156.2.c.c	$2156$	$2$	2156.c	77.b	$2$	$16$	$16$	$17.216$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					308.2.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{5}q^{9}-\beta _{11}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)