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

• Label: 380.3.h
• Level: $380$
• Weight: $3$
• Character orbit: 380.h
• Rep. character: $\chi_{380}(39,\cdot)$
• Character field: $\Q$
• Dimension: $108$
• 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.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
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	124	108	16
Cusp forms	116	108	8
Eisenstein series	8	0	8

Trace form

108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * 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.h.a	$380$	$3$	380.h	20.d	$2$	$108$	$108$	$10.354$		None		✓	✓	✓	380.3.h.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{3}^{\mathrm{old}}(380, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)