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

• Label: 441.2.g
• Level: $441$
• Weight: $2$
• Character orbit: 441.g
• Rep. character: $\chi_{441}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $8$
• Sturm bound: $112$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(112\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	128	88	40
Cusp forms	96	72	24
Eisenstein series	32	16	16

Trace form

\( 72 q - q^{2} + q^{3} - 33 q^{4} + 10 q^{5} + 2 q^{6} - 12 q^{8} - q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.2.g.a	$441$	$2$	441.g	63.g	$3$	$2$	$1$	$3.521$	\(\Q(\sqrt{-3}) \)	None					63.2.g.a	$2$	$0$	\(-1\)	\(3\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.g.b	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	\(\Q(\zeta_{18})\)	None					63.2.f.a	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}+\beta_1-1)q^{2}+(\beta_{4}+\beta_{2})q^{3}+\cdots\)
441.2.g.c	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	\(\Q(\zeta_{18})\)	None					63.2.f.a	$2$	$0$	\(-3\)	\(0\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}+\beta_1-1)q^{2}+(-\beta_{4}-\beta_{2})q^{3}+\cdots\)
441.2.g.d	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	6.0.309123.1	None					63.2.f.b	$2$	$0$	\(1\)	\(-2\)	\(10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-1+\cdots)q^{3}+\cdots\)
441.2.g.e	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	6.0.309123.1	None					63.2.f.b	$2$	$0$	\(1\)	\(2\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(1-\beta _{1}+\cdots)q^{3}+\cdots\)
441.2.g.f	$441$	$2$	441.g	63.g	$3$	$10$	$5$	$3.521$	10.0.\(\cdots\).1	None					63.2.g.b	$2$	$0$	\(2\)	\(-2\)	\(8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.g.g	$441$	$2$	441.g	63.g	$3$	$12$	$6$	$3.521$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			441.2.f.g	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}+\beta _{5})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
441.2.g.h	$441$	$2$	441.g	63.g	$3$	$24$	$12$	$3.521$		None		✓	✓		441.2.f.h	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

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