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

• Label: 441.2.h
• Level: $441$
• Weight: $2$
• Character orbit: 441.h
• Rep. character: $\chi_{441}(214,\cdot)$
• 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.h (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

\( 72 q + 2 q^{2} + q^{3} + 66 q^{4} - 5 q^{5} + 2 q^{6} - 12 q^{8} - 7 q^{9} + O(q^{10}) \)

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

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

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