Space of modular forms of level 380, weight 2, and Character 380.k

• Label: 380.2.k
• Level: $380$
• Weight: $2$
• Character orbit: 380.k
• Rep. character: $\chi_{380}(267,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $108$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

	Total	New	Old
Modular forms	128	108	20
Cusp forms	112	108	4
Eisenstein series	16	0	16

Trace form

108 * q - 16 * q^10 - 16 * q^12 - 4 * q^13 + 16 * q^16 - 20 * q^17 - 16 * q^21 - 16 * q^22 - 20 * q^25 - 32 * q^28 - 24 * q^30 - 40 * q^32 + 16 * q^33 - 16 * q^36 + 20 * q^37 + 24 * q^40 + 20 * q^45 - 48 * q^46 - 20 * q^48 + 4 * q^50 + 20 * q^52 - 44 * q^53 - 8 * q^56 - 32 * q^58 - 20 * q^60 + 24 * q^62 + 20 * q^65 + 72 * q^66 + 8 * q^68 + 76 * q^70 + 100 * q^72 + 36 * q^73 + 24 * q^77 + 24 * q^78 - 96 * q^80 - 28 * q^81 - 24 * q^82 + 4 * q^85 + 32 * q^86 - 20 * q^88 - 16 * q^90 - 40 * q^92 + 48 * q^93 - 40 * q^96 - 60 * q^97 - 64 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.2.k.a	$380$	$2$	380.k	20.e	$4$	$2$	$1$	$3.034$	\(\Q(\sqrt{-1}) \)	None		✓			380.2.k.a	$2$	$0$	\(-2\)	\(-2\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}+(-i-1)q^{3}-2 i q^{4}+\cdots\)
380.2.k.b	$380$	$2$	380.k	20.e	$4$	$2$	$1$	$3.034$	\(\Q(\sqrt{-1}) \)	None		✓			380.2.k.a	$2$	$0$	\(2\)	\(2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}+(i+1)q^{3}-2 i q^{4}+\cdots\)
380.2.k.c	$380$	$2$	380.k	20.e	$4$	$52$	$26$	$3.034$		None		✓			380.2.k.c	$2$	$0$	\(-2\)	\(-2\)	\(4\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
380.2.k.d	$380$	$2$	380.k	20.e	$4$	$52$	$26$	$3.034$		None		✓			380.2.k.c	$2$	$0$	\(2\)	\(2\)	\(4\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

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