Space of modular forms of level 1386, weight 2, and Character 1386.c

• Label: 1386.2.c
• Level: $1386$
• Weight: $2$
• Character orbit: 1386.c
• Rep. character: $\chi_{1386}(197,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

	Total	New	Old
Modular forms	304	24	280
Cusp forms	272	24	248
Eisenstein series	32	0	32

Trace form

\( 24 q + 24 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1386.2.c.a	$1386$	$2$	1386.c	33.d	$2$	$12$	$12$	$11.067$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}-\beta _{1}q^{7}+\cdots\)
1386.2.c.b	$1386$	$2$	1386.c	33.d	$2$	$12$	$12$	$11.067$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \)