Space of modular forms of level 441, weight 3, and Character 441.j

• Label: 441.3.j
• Level: $441$
• Weight: $3$
• Character orbit: 441.j
• Rep. character: $\chi_{441}(263,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $152$
• Newform subspaces: $9$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(441, [\chi])\).

	Total	New	Old
Modular forms	240	168	72
Cusp forms	208	152	56
Eisenstein series	32	16	16

Trace form

\( 152 q + q^{3} - 286 q^{4} + 3 q^{5} + 8 q^{6} - 19 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(441, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.3.j.a	$441$	$3$	441.j	63.j	$6$	$2$	$1$	$12.016$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}+\cdots\)
441.3.j.b	$441$	$3$	441.j	63.j	$6$	$2$	$1$	$12.016$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}+q^{4}+\cdots\)
441.3.j.c	$441$	$3$	441.j	63.j	$6$	$6$	$3$	$12.016$	6.0.63369648.1	None		$2$	$0$	\(0\)	\(-18\)	\(15\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{4}-\beta _{5})q^{2}-3q^{3}+(-4+\cdots)q^{4}+\cdots\)
441.3.j.d	$441$	$3$	441.j	63.j	$6$	$8$	$4$	$12.016$	8.0.3317760000.3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5})q^{2}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
441.3.j.e	$441$	$3$	441.j	63.j	$6$	$16$	$8$	$12.016$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{8}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
441.3.j.f	$441$	$3$	441.j	63.j	$6$	$22$	$11$	$12.016$		None		$2$	$0$	\(0\)	\(19\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
441.3.j.g	$441$	$3$	441.j	63.j	$6$	$24$	$12$	$12.016$		None		$2$	$0$	\(0\)	\(-8\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
441.3.j.h	$441$	$3$	441.j	63.j	$6$	$24$	$12$	$12.016$		None		$2$	$0$	\(0\)	\(8\)	\(18\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
441.3.j.i	$441$	$3$	441.j	63.j	$6$	$48$	$24$	$12.016$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)