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

• Label: 784.2.bk
• Level: $784$
• Weight: $2$
• Character orbit: 784.bk
• Rep. character: $\chi_{784}(27,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $1320$
• 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.bk (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 784 \)
Character field:			\(\Q(\zeta_{28})\)
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	1368	1368	0
Cusp forms	1320	1320	0
Eisenstein series	48	48	0

Trace form

1320 * q - 10 * q^2 - 14 * q^3 - 10 * q^4 - 14 * q^5 - 14 * q^6 - 24 * q^7 + 2 * q^8 - 14 * q^10 - 10 * q^11 - 14 * q^12 - 14 * q^13 - 16 * q^14 - 10 * q^16 - 28 * q^17 - 12 * q^18 - 14 * q^20 - 18 * q^21 - 34 * q^22 - 20 * q^23 - 14 * q^24 - 14 * q^26 - 14 * q^27 - 66 * q^28 - 10 * q^29 - 32 * q^30 + 10 * q^32 - 28 * q^33 - 126 * q^34 - 10 * q^35 - 26 * q^36 - 10 * q^37 - 14 * q^38 - 20 * q^39 - 126 * q^40 + 26 * q^42 - 10 * q^43 - 14 * q^44 - 14 * q^45 - 22 * q^46 - 24 * q^49 - 44 * q^50 + 18 * q^51 - 14 * q^52 - 10 * q^53 - 14 * q^54 - 28 * q^55 - 132 * q^56 - 70 * q^58 - 14 * q^59 + 114 * q^60 - 14 * q^61 - 42 * q^62 - 46 * q^64 - 20 * q^65 - 154 * q^66 - 14 * q^69 - 22 * q^70 + 140 * q^71 - 42 * q^72 - 54 * q^74 - 14 * q^75 - 224 * q^76 + 2 * q^77 + 50 * q^78 + 168 * q^81 - 154 * q^82 - 14 * q^83 - 248 * q^84 - 30 * q^85 + 20 * q^86 - 28 * q^87 + 100 * q^88 - 14 * q^90 + 134 * q^91 + 56 * q^92 - 40 * q^93 + 154 * q^94 - 28 * q^96 - 32 * q^98 - 72 * q^99

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.bk.a	$784$	$2$	784.bk	784.ak	$28$	$1320$	$110$	$6.260$		None		✓	✓	✓	784.2.bk.a	$4$	$0$	\(-10\)	\(-14\)	\(-14\)	\(-24\)		$\mathrm{SU}(2)[C_{28}]$