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

• Label: 380.3.j
• Level: $380$
• Weight: $3$
• Character orbit: 380.j
• Rep. character: $\chi_{380}(227,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $232$
• 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.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q(i)\)
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	248	0
Cusp forms	232	232	0
Eisenstein series	16	16	0

Trace form

232 * q - 8 * q^5 - 32 * q^6 - 64 * q^16 - 8 * q^17 + 80 * q^20 - 8 * q^25 + 40 * q^26 + 40 * q^28 - 104 * q^30 + 104 * q^36 + 184 * q^38 + 192 * q^42 + 192 * q^45 + 280 * q^58 + 112 * q^61 - 280 * q^62 + 216 * q^66 - 248 * q^68 - 8 * q^73 - 128 * q^76 + 336 * q^77 - 144 * q^80 - 1528 * q^81 + 552 * q^82 + 136 * q^85 + 552 * q^92 - 272 * q^93 + 504 * q^96

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.j.a	$380$	$3$	380.j	380.j	$4$	$232$	$116$	$10.354$		None		✓	✓	✓	380.3.j.a	$8$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$