Space of modular forms of level 381, weight 2, and Character 381.i

• Label: 381.2.i
• Level: $381$
• Weight: $2$
• Character orbit: 381.i
• Rep. character: $\chi_{381}(4,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $132$
• Newform subspaces: $2$
• Sturm bound: $85$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.i (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 127 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(85\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(381, [\chi])\).

	Total	New	Old
Modular forms	264	132	132
Cusp forms	240	132	108
Eisenstein series	24	0	24

Trace form

\( 132 q + 10 q^{2} - 2 q^{3} - 14 q^{4} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(381, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
381.2.i.a	$381$	$2$	381.i	127.e	$7$	$60$	$10$	$3.042$		None		$2$	$0$	\(6\)	\(10\)	\(4\)	\(-14\)		$\mathrm{SU}(2)[C_{7}]$
381.2.i.b	$381$	$2$	381.i	127.e	$7$	$72$	$12$	$3.042$		None		$2$	$0$	\(4\)	\(-12\)	\(-4\)	\(16\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 2}\)