Space of modular forms of level 387, weight 2, and Character 387.u

• Label: 387.2.u
• Level: $387$
• Weight: $2$
• Character orbit: 387.u
• Rep. character: $\chi_{387}(64,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $108$
• Newform subspaces: $6$
• Sturm bound: $88$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.u (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(88\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(387, [\chi])\).

	Total	New	Old
Modular forms	288	120	168
Cusp forms	240	108	132
Eisenstein series	48	12	36

Trace form

\( 108 q + 6 q^{2} - 22 q^{4} + 5 q^{5} - 24 q^{7} - 10 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(387, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
387.2.u.a	$387$	$2$	387.u	43.e	$7$	$6$	$1$	$3.090$	\(\Q(\zeta_{14})\)	None		$2$	$1$	\(-3\)	\(0\)	\(-2\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-\zeta_{14}-\zeta_{14}^{3}-\zeta_{14}^{5})q^{2}+(-1+\cdots)q^{4}+\cdots\)
387.2.u.b	$387$	$2$	387.u	43.e	$7$	$6$	$1$	$3.090$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(5\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
387.2.u.c	$387$	$2$	387.u	43.e	$7$	$6$	$1$	$3.090$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(5\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
387.2.u.d	$387$	$2$	387.u	43.e	$7$	$12$	$2$	$3.090$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(10\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\beta _{2}+\beta _{6}+\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{2}+\cdots\)
387.2.u.e	$387$	$2$	387.u	43.e	$7$	$30$	$5$	$3.090$		None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(2\)		$\mathrm{SU}(2)[C_{7}]$
387.2.u.f	$387$	$2$	387.u	43.e	$7$	$48$	$8$	$3.090$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

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