Space of modular forms of level 784, weight 2, and Character 784.bu

• Label: 784.2.bu
• Level: $784$
• Weight: $2$
• Character orbit: 784.bu
• Rep. character: $\chi_{784}(3,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $2640$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bu (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 784 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).

	Total	New	Old
Modular forms	2736	2736	0
Cusp forms	2640	2640	0
Eisenstein series	96	96	0

Trace form

2640 * q - 26 * q^2 - 22 * q^3 - 26 * q^4 - 22 * q^5 - 28 * q^6 - 48 * q^7 - 32 * q^8 - 4 * q^10 - 26 * q^11 - 22 * q^12 - 28 * q^13 - 44 * q^14 - 26 * q^16 - 44 * q^17 + 6 * q^18 - 36 * q^19 - 28 * q^20 - 18 * q^21 + 4 * q^22 - 52 * q^23 - 22 * q^24 - 22 * q^26 - 28 * q^27 + 30 * q^28 - 20 * q^29 - 16 * q^30 - 16 * q^32 - 44 * q^33 + 84 * q^34 - 26 * q^35 - 4 * q^36 - 26 * q^37 - 22 * q^38 - 52 * q^39 + 150 * q^40 - 98 * q^42 - 20 * q^43 - 112 * q^44 - 40 * q^45 - 44 * q^46 - 48 * q^49 - 28 * q^50 + 6 * q^51 - 112 * q^52 - 26 * q^53 - 70 * q^54 - 56 * q^55 + 96 * q^56 - 56 * q^58 - 70 * q^59 - 258 * q^60 - 22 * q^61 + 16 * q^64 - 52 * q^65 - 14 * q^66 - 66 * q^68 - 28 * q^69 + 52 * q^70 - 200 * q^71 - 42 * q^72 - 48 * q^74 - 52 * q^75 + 182 * q^76 - 38 * q^77 - 80 * q^78 + 72 * q^80 - 240 * q^81 + 70 * q^82 - 28 * q^83 - 184 * q^84 - 32 * q^86 - 44 * q^87 + 260 * q^88 - 28 * q^90 - 212 * q^91 - 44 * q^92 + 4 * q^93 - 154 * q^94 + 664 * q^96 + 38 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
784.2.bu.a	$784$	$2$	784.bu	784.au	$84$	$2640$	$110$	$6.260$		None		✓	✓	✓	784.2.bu.a	$4$	$0$	\(-26\)	\(-22\)	\(-22\)	\(-48\)		$\mathrm{SU}(2)[C_{84}]$