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 + 6 * q^10 + 3 * q^11 + 20 * q^12 + 3 * q^13 + 10 * q^15 + 54 * q^16 - 9 * q^17 - 26 * q^18 - 4 * q^20 + 4 * q^23 - 6 * q^24 - 21 * q^25 - 16 * q^26 + 7 * q^27 - 18 * q^29 - 15 * q^30 - 6 * q^31 - 82 * q^32 - 29 * q^33 - 70 * q^36 + 3 * q^37 - 19 * q^38 + 11 * q^39 + 6 * q^40 - 10 * q^41 - 11 * q^44 + 19 * q^45 - 12 * q^46 + 54 * q^47 + 5 * q^48 - 45 * q^50 + 58 * q^51 + 15 * q^52 + 16 * q^53 - q^54 + 6 * q^55 - 15 * q^57 + 9 * q^58 + 60 * q^59 + 5 * q^60 + 12 * q^62 + 12 * q^64 - 60 * q^65 - 34 * q^66 - 12 * q^67 - 30 * q^68 - 6 * q^69 + 6 * q^71 - 36 * q^72 - 12 * q^73 + 41 * q^74 + 26 * q^75 - 6 * q^76 + 69 * q^78 - 36 * q^79 - 19 * q^80 - 55 * q^81 - 18 * q^83 + 3 * q^85 + 25 * q^86 - 5 * q^87 - 9 * q^88 - 41 * q^89 - 25 * q^90 - 52 * q^92 - 50 * q^93 - 6 * q^94 + 34 * q^95 - 59 * q^96 + 3 * q^97 - 34 * q^99

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.h.a	$441$	$2$	441.h	63.h	$3$	$2$	$1$	$3.521$	\(\Q(\sqrt{-3}) \)	None					63.2.g.a	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
441.2.h.b	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	6.0.309123.1	None					63.2.f.b	$2$	$0$	\(-2\)	\(-2\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+\cdots\)
441.2.h.c	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	6.0.309123.1	None					63.2.f.b	$2$	$0$	\(-2\)	\(2\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
441.2.h.d	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	\(\Q(\zeta_{18})\)	None					63.2.f.a	$2$	$0$	\(6\)	\(0\)	\(-3\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_{4}-\beta_{3}+1)q^{2}+(\beta_{5}+\beta_{2})q^{3}+\cdots\)
441.2.h.e	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	\(\Q(\zeta_{18})\)	None					63.2.f.a	$2$	$0$	\(6\)	\(0\)	\(3\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_{4}-\beta_{3}+1)q^{2}+(-\beta_{5}-\beta_{2})q^{3}+\cdots\)
441.2.h.f	$441$	$2$	441.h	63.h	$3$	$10$	$5$	$3.521$	10.0.\(\cdots\).1	None					63.2.g.b	$2$	$0$	\(-4\)	\(1\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.h.g	$441$	$2$	441.h	63.h	$3$	$12$	$6$	$3.521$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			441.2.f.g	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+\cdots\)
441.2.h.h	$441$	$2$	441.h	63.h	$3$	$24$	$12$	$3.521$		None		✓	✓		441.2.f.h	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

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