Space of modular forms of level 832, weight 2, and Character 832.by

• Label: 832.2.by
• Level: $832$
• Weight: $2$
• Character orbit: 832.by
• Rep. character: $\chi_{832}(53,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $768$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.by (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(832, [\chi])\).

	Total	New	Old
Modular forms	912	768	144
Cusp forms	880	768	112
Eisenstein series	32	0	32

Trace form

768 * q - 16 * q^22 - 80 * q^24 - 160 * q^30 - 160 * q^36 - 80 * q^42 - 16 * q^44 + 48 * q^50 - 64 * q^51 + 128 * q^54 - 64 * q^55 + 112 * q^56 + 48 * q^62 - 160 * q^63 + 192 * q^64 + 192 * q^66 - 160 * q^67 + 48 * q^68 + 112 * q^74 - 64 * q^75 + 128 * q^76 - 64 * q^79 + 48 * q^80 - 224 * q^84 - 304 * q^92 - 192 * q^94 - 272 * q^96 - 272 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(832, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.2.by.a	$832$	$2$	832.by	64.i	$16$	$768$	$96$	$6.644$		None		✓	✓	✓	832.2.by.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)