Space of modular forms of level 1856, weight 2, and Character 1856.c

• Label: 1856.2.c
• Level: $1856$
• Weight: $2$
• Character orbit: 1856.c
• Rep. character: $\chi_{1856}(929,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $480$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1856.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(480\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1856, [\chi])\).

	Total	New	Old
Modular forms	252	56	196
Cusp forms	228	56	172
Eisenstein series	24	0	24

Trace form

\( 56 q - 56 q^{9} - 56 q^{25} - 48 q^{33} + 48 q^{41} + 88 q^{49} + 16 q^{57} - 32 q^{73} + 8 q^{81} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1856, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1856.2.c.a	$1856$	$2$	1856.c	8.b	$2$	$8$	$8$	$14.820$	8.0.214798336.3	None		✓			1856.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1856.2.c.b	$1856$	$2$	1856.c	8.b	$2$	$8$	$8$	$14.820$	8.0.214798336.3	None		✓			1856.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{3}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1856.2.c.c	$1856$	$2$	1856.c	8.b	$2$	$20$	$20$	$14.820$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			1856.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{13}q^{3}+\beta _{17}q^{5}+(-1+\beta _{8})q^{7}+\cdots\)
1856.2.c.d	$1856$	$2$	1856.c	8.b	$2$	$20$	$20$	$14.820$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			1856.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{13}q^{3}-\beta _{17}q^{5}+(1-\beta _{8})q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)