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

• Label: 832.2.ct
• Level: $832$
• Weight: $2$
• Character orbit: 832.ct
• Rep. character: $\chi_{832}(115,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $1760$
• 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.ct (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 832 \)
Character field:			\(\Q(\zeta_{48})\)
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	1824	1824	0
Cusp forms	1760	1760	0
Eisenstein series	64	64	0

Trace form

1760 * q - 16 * q^2 - 8 * q^3 - 24 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 8 * q^9 - 24 * q^10 - 16 * q^11 - 64 * q^12 - 16 * q^13 - 32 * q^14 - 24 * q^15 - 8 * q^16 - 24 * q^17 - 16 * q^18 - 16 * q^19 + 16 * q^20 - 16 * q^21 - 8 * q^22 - 24 * q^23 - 16 * q^24 - 16 * q^26 - 32 * q^27 - 96 * q^28 - 8 * q^29 - 56 * q^30 - 32 * q^31 - 56 * q^32 + 8 * q^34 - 8 * q^35 - 24 * q^36 - 16 * q^37 + 80 * q^39 - 32 * q^40 - 16 * q^41 - 8 * q^42 - 24 * q^43 - 16 * q^44 - 40 * q^45 + 48 * q^46 - 320 * q^48 - 24 * q^49 - 120 * q^50 + 112 * q^52 - 32 * q^53 - 16 * q^54 - 72 * q^55 + 56 * q^56 - 16 * q^57 - 88 * q^58 + 48 * q^59 + 48 * q^60 - 8 * q^61 - 24 * q^62 - 32 * q^65 - 32 * q^66 - 16 * q^67 + 40 * q^68 - 24 * q^69 + 248 * q^70 + 48 * q^71 - 88 * q^72 - 16 * q^73 - 8 * q^74 + 16 * q^75 + 48 * q^76 - 40 * q^78 - 32 * q^79 + 48 * q^80 - 8 * q^81 - 24 * q^82 - 16 * q^83 + 136 * q^84 + 64 * q^85 - 160 * q^86 - 8 * q^87 - 24 * q^88 - 16 * q^89 - 96 * q^90 - 16 * q^91 - 32 * q^92 + 8 * q^93 + 40 * q^94 - 48 * q^95 - 160 * q^96 - 296 * q^99

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.ct.a	$832$	$2$	832.ct	832.bt	$48$	$1760$	$110$	$6.644$		None		✓	✓	✓	832.2.cn.a	$2$	$0$	\(-16\)	\(-8\)	\(-16\)	\(-16\)		$\mathrm{SU}(2)[C_{48}]$