Space of modular forms of level 441, weight 4, and Character 441.p

• Label: 441.4.p
• Level: $441$
• Weight: $4$
• Character orbit: 441.p
• Rep. character: $\chi_{441}(80,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

	Total	New	Old
Modular forms	368	80	288
Cusp forms	304	80	224
Eisenstein series	64	0	64

Trace form

\( 80 q + 160 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.4.p.a	$441$	$4$	441.p	21.g	$6$	$8$	$4$	$26.020$	8.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{4}q^{2}+(\beta _{2}-\beta _{5})q^{5}+(2^{4}\beta _{3}+2^{4}\beta _{4}+\cdots)q^{8}+\cdots\)
441.4.p.b	$441$	$4$	441.p	21.g	$6$	$8$	$4$	$26.020$	8.0.\(\cdots\).5	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{3}q^{2}+(8+5\beta _{1}-8\beta _{2}+5\beta _{4})q^{4}+\cdots\)
441.4.p.c	$441$	$4$	441.p	21.g	$6$	$16$	$8$	$26.020$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(4+\beta _{2}-4\beta _{3}+\beta _{9})q^{4}+\cdots\)
441.4.p.d	$441$	$4$	441.p	21.g	$6$	$48$	$24$	$26.020$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)