Space of modular forms of level 380, weight 3, and Character 380.q

• Label: 380.3.q
• Level: $380$
• Weight: $3$
• Character orbit: 380.q
• Rep. character: $\chi_{380}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(380, [\chi])\).

	Total	New	Old
Modular forms	248	160	88
Cusp forms	232	160	72
Eisenstein series	16	0	16

Trace form

160 * q + 2 * q^4 + 6 * q^6 + 248 * q^9 - 10 * q^10 - 16 * q^13 - 14 * q^16 + 48 * q^17 + 48 * q^21 - 44 * q^24 - 400 * q^25 + 68 * q^26 + 60 * q^28 - 80 * q^30 + 30 * q^32 - 40 * q^33 - 22 * q^34 + 52 * q^36 + 160 * q^37 + 130 * q^38 - 80 * q^40 - 112 * q^41 - 122 * q^42 - 208 * q^44 - 388 * q^46 + 342 * q^48 - 1168 * q^49 + 170 * q^52 - 16 * q^53 - 6 * q^54 - 168 * q^56 - 308 * q^58 - 30 * q^60 + 224 * q^61 + 448 * q^62 - 448 * q^64 + 160 * q^65 + 108 * q^66 - 532 * q^68 + 384 * q^69 - 60 * q^70 + 512 * q^72 + 264 * q^73 + 252 * q^74 - 720 * q^76 + 160 * q^77 + 80 * q^78 + 160 * q^80 - 1072 * q^81 + 458 * q^82 + 216 * q^84 - 160 * q^85 + 96 * q^86 + 1412 * q^88 - 184 * q^89 + 30 * q^90 + 984 * q^92 - 144 * q^93 + 36 * q^94 + 312 * q^96 + 744 * q^97 - 226 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(380, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.3.q.a	$380$	$3$	380.q	76.g	$6$	$160$	$80$	$10.354$		None		✓	✓	✓	380.3.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(380, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)