Space of modular forms of level 387, weight 5, and Character 387.b

• Label: 387.5.b
• Level: $387$
• Weight: $5$
• Character orbit: 387.b
• Rep. character: $\chi_{387}(343,\cdot)$
• Character field: $\Q$
• Dimension: $73$
• Newform subspaces: $5$
• Sturm bound: $220$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	387.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(220\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(387, [\chi])\).

	Total	New	Old
Modular forms	180	75	105
Cusp forms	172	73	99
Eisenstein series	8	2	6

Trace form

\( 73 q - 588 q^{4} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(387, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
387.5.b.a	$387$	$5$	387.b	43.b	$2$	$1$	$1$	$40.004$	\(\Q\)	\(\Q(\sqrt{-43}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}-199q^{11}-7^{2}q^{13}+2^{8}q^{16}+\cdots\)
387.5.b.b	$387$	$5$	387.b	43.b	$2$	$2$	$2$	$40.004$	\(\Q(\sqrt{43}) \)	\(\Q(\sqrt{-43}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}-7\beta q^{11}+7^{2}q^{13}+2^{8}q^{16}+\cdots\)
387.5.b.c	$387$	$5$	387.b	43.b	$2$	$12$	$12$	$40.004$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-8+\beta _{2})q^{4}+(-\beta _{1}+\beta _{9}+\cdots)q^{5}+\cdots\)
387.5.b.d	$387$	$5$	387.b	43.b	$2$	$28$	$28$	$40.004$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
387.5.b.e	$387$	$5$	387.b	43.b	$2$	$30$	$30$	$40.004$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(387, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)