Space of modular forms of level 656, weight 2, and Character 656.n

• Label: 656.2.n
• Level: $656$
• Weight: $2$
• Character orbit: 656.n
• Rep. character: $\chi_{656}(165,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $160$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(656, [\chi])\).

	Total	New	Old
Modular forms	172	160	12
Cusp forms	164	160	4
Eisenstein series	8	0	8

Trace form

160 * q - 4 * q^4 + 8 * q^10 - 8 * q^11 + 12 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 12 * q^20 + 4 * q^22 - 4 * q^24 - 12 * q^26 - 16 * q^29 - 28 * q^30 - 40 * q^32 - 40 * q^34 - 32 * q^36 - 16 * q^37 + 52 * q^40 + 20 * q^42 + 8 * q^43 + 4 * q^44 - 40 * q^47 + 20 * q^48 - 160 * q^49 + 4 * q^50 - 24 * q^51 - 4 * q^52 + 16 * q^53 + 76 * q^54 + 28 * q^56 + 12 * q^58 + 32 * q^59 + 76 * q^60 + 32 * q^61 - 80 * q^62 + 40 * q^63 - 28 * q^64 - 28 * q^66 + 40 * q^67 - 24 * q^68 + 32 * q^69 + 68 * q^70 + 12 * q^72 - 56 * q^75 + 16 * q^77 - 24 * q^78 - 8 * q^79 - 28 * q^80 - 160 * q^81 + 32 * q^84 - 32 * q^85 + 4 * q^86 - 20 * q^88 + 80 * q^90 - 32 * q^91 + 8 * q^92 + 76 * q^94 + 64 * q^95 + 28 * q^96 + 68 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(656, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
656.2.n.a	$656$	$2$	656.n	16.e	$4$	$2$	$1$	$5.238$	\(\Q(\sqrt{-1}) \)	None		✓			656.2.n.a	$2$	$0$	\(2\)	\(-4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}+(2 i-2)q^{3}-2 i q^{4}+\cdots\)
656.2.n.b	$656$	$2$	656.n	16.e	$4$	$2$	$1$	$5.238$	\(\Q(\sqrt{-1}) \)	None		✓			656.2.n.b	$2$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}-2 i q^{4}+(i+1)q^{5}+\cdots\)
656.2.n.c	$656$	$2$	656.n	16.e	$4$	$2$	$1$	$5.238$	\(\Q(\sqrt{-1}) \)	None		✓			656.2.n.c	$2$	$0$	\(2\)	\(4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}+(-2 i+2)q^{3}-2 i q^{4}+\cdots\)
656.2.n.d	$656$	$2$	656.n	16.e	$4$	$4$	$2$	$5.238$	\(\Q(\zeta_{12})\)	None		✓			656.2.n.d	$2$	$1$	\(-4\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_1-1)q^{2}+(-\beta_1-1)q^{3}+\cdots\)
656.2.n.e	$656$	$2$	656.n	16.e	$4$	$4$	$2$	$5.238$	\(\Q(i, \sqrt{7})\)	None		✓			656.2.n.e	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
656.2.n.f	$656$	$2$	656.n	16.e	$4$	$66$	$33$	$5.238$		None		✓			656.2.n.f	$2$	$0$	\(-2\)	\(8\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
656.2.n.g	$656$	$2$	656.n	16.e	$4$	$80$	$40$	$5.238$		None		✓	✓		656.2.n.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(656, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(656, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)