Space of modular forms of level 832, weight 3, and Character 832.q

• Label: 832.3.q
• Level: $832$
• Weight: $3$
• Character orbit: 832.q
• Rep. character: $\chi_{832}(79,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	832.q (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(832, [\chi])\).

	Total	New	Old
Modular forms	464	96	368
Cusp forms	432	96	336
Eisenstein series	32	0	32

Trace form

96 * q - 32 * q^11 + 64 * q^19 + 128 * q^23 + 32 * q^29 - 96 * q^35 - 96 * q^37 - 160 * q^43 + 672 * q^49 + 352 * q^51 - 160 * q^53 + 256 * q^55 - 64 * q^61 - 448 * q^67 + 192 * q^69 - 416 * q^75 + 224 * q^77 - 864 * q^81 + 480 * q^83 + 320 * q^85 + 896 * q^87 - 480 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(832, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.3.q.a	$832$	$3$	832.q	16.f	$4$	$96$	$48$	$22.670$		None			✓	✓	208.3.q.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)