Space of modular forms of level 440, weight 3, and Character 440.br

• Label: 440.3.br
• Level: $440$
• Weight: $3$
• Character orbit: 440.br
• Rep. character: $\chi_{440}(83,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1120$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	440.br (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 440 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(440, [\chi])\).

	Total	New	Old
Modular forms	1184	1184	0
Cusp forms	1120	1120	0
Eisenstein series	64	64	0

Trace form

1120 * q - 10 * q^2 - 12 * q^3 - 20 * q^6 - 10 * q^8 - 32 * q^11 - 100 * q^12 + 12 * q^16 - 20 * q^17 - 10 * q^18 + 28 * q^20 + 10 * q^22 - 12 * q^25 + 28 * q^26 - 84 * q^27 - 10 * q^28 - 370 * q^30 + 20 * q^33 - 20 * q^35 + 196 * q^36 + 38 * q^38 - 10 * q^40 - 40 * q^41 + 78 * q^42 - 380 * q^46 + 30 * q^48 - 10 * q^50 - 40 * q^51 + 510 * q^52 - 952 * q^56 - 20 * q^57 - 250 * q^58 - 2 * q^60 - 460 * q^62 - 244 * q^66 - 32 * q^67 - 10 * q^68 + 94 * q^70 - 1060 * q^72 - 20 * q^73 - 12 * q^75 - 716 * q^78 + 414 * q^80 + 1920 * q^81 + 326 * q^82 + 780 * q^83 + 476 * q^86 + 190 * q^88 - 820 * q^90 - 408 * q^91 + 496 * q^92 + 1800 * q^96 + 52 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(440, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
440.3.br.a	$440$	$3$	440.br	440.ar	$20$	$1120$	$140$	$11.989$		None		✓	✓	✓	440.3.br.a	$8$	$0$	\(-10\)	\(-12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$