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

• Label: 380.3.p
• Level: $380$
• Weight: $3$
• Character orbit: 380.p
• Rep. character: $\chi_{380}(159,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
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	248	0
Cusp forms	232	232	0
Eisenstein series	16	16	0

Trace form

232 * q - 2 * q^5 + 8 * q^6 - 328 * q^9 + 20 * q^14 + 12 * q^16 + 92 * q^20 - 40 * q^21 - 134 * q^24 - 2 * q^25 + 28 * q^26 - 4 * q^29 + 268 * q^30 - 70 * q^34 + 12 * q^36 - 42 * q^40 - 12 * q^41 + 98 * q^44 + 128 * q^45 + 68 * q^46 + 1320 * q^49 - 156 * q^50 - 44 * q^54 - 400 * q^56 + 146 * q^60 - 68 * q^61 - 324 * q^64 - 204 * q^65 + 58 * q^66 + 440 * q^69 + 62 * q^70 - 212 * q^74 + 246 * q^76 + 28 * q^80 - 1116 * q^81 + 96 * q^84 - 46 * q^85 - 28 * q^86 - 60 * q^89 + 482 * q^90 - 756 * q^94 - 628 * 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.p.a	$380$	$3$	380.p	380.p	$6$	$232$	$116$	$10.354$		None		✓	✓	✓	380.3.p.a	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$