Space of modular forms of level 221, weight 2, and Character 221.m

• Label: 221.2.m
• Level: $221$
• Weight: $2$
• Character orbit: 221.m
• Rep. character: $\chi_{221}(69,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $42$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(42\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(221, [\chi])\).

	Total	New	Old
Modular forms	48	36	12
Cusp forms	40	36	4
Eisenstein series	8	0	8

Trace form

36 * q + 2 * q^3 + 16 * q^4 - 18 * q^6 - 6 * q^7 - 16 * q^9 + 4 * q^10 - 12 * q^11 + 4 * q^12 + 6 * q^13 - 8 * q^14 + 6 * q^15 - 20 * q^16 - 4 * q^17 + 6 * q^19 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 40 * q^25 - 50 * q^26 - 4 * q^27 - 12 * q^28 + 2 * q^29 + 20 * q^30 + 66 * q^32 - 12 * q^33 + 4 * q^35 + 18 * q^36 + 6 * q^37 - 56 * q^38 - 50 * q^39 + 4 * q^40 - 18 * q^41 - 44 * q^42 + 32 * q^43 + 30 * q^45 + 60 * q^46 - 4 * q^48 + 16 * q^49 + 48 * q^50 + 16 * q^51 + 26 * q^52 + 8 * q^53 + 90 * q^54 - 4 * q^55 + 26 * q^56 - 84 * q^58 + 18 * q^59 + 10 * q^61 - 36 * q^62 - 30 * q^63 - 28 * q^64 + 28 * q^65 + 48 * q^66 - 42 * q^67 + 12 * q^68 - 10 * q^69 + 30 * q^71 - 18 * q^72 - 8 * q^74 + 18 * q^75 + 42 * q^76 + 4 * q^77 - 10 * q^78 + 16 * q^79 + 66 * q^80 - 70 * q^81 - 30 * q^82 - 96 * q^84 - 6 * q^85 - 14 * q^87 + 20 * q^88 - 42 * q^89 - 20 * q^90 - 6 * q^91 - 88 * q^92 + 48 * q^93 + 14 * q^94 + 20 * q^95 - 36 * q^97 - 24 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(221, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
221.2.m.a	$221$	$2$	221.m	13.e	$6$	$2$	$1$	$1.765$	\(\Q(\sqrt{-3}) \)	None		✓			221.2.m.a	$2$	$0$	\(3\)	\(1\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
221.2.m.b	$221$	$2$	221.m	13.e	$6$	$12$	$6$	$1.765$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			221.2.m.b	$2$	$0$	\(-3\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
221.2.m.c	$221$	$2$	221.m	13.e	$6$	$22$	$11$	$1.765$		None		✓	✓		221.2.m.c	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(221, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(221, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)