Space of modular forms of level 441, weight 2, and Character 441.c

• Label: 441.2.c
• Level: $441$
• Weight: $2$
• Character orbit: 441.c
• Rep. character: $\chi_{441}(440,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	40	12	28
Eisenstein series	32	0	32

Trace form

\( 12 q - 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.2.c.a	$441$	$2$	441.c	21.c	$2$	$4$	$4$	$3.521$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots\)
441.2.c.b	$441$	$2$	441.c	21.c	$2$	$8$	$8$	$3.521$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{16}-\zeta_{16}^{2})q^{2}+(-1+2\zeta_{16}^{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

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