Space of modular forms of level 273, weight 2, and Character 273.k

• Label: 273.2.k
• Level: $273$
• Weight: $2$
• Character orbit: 273.k
• Rep. character: $\chi_{273}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $74$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(74\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

	Total	New	Old
Modular forms	84	24	60
Cusp forms	68	24	44
Eisenstein series	16	0	16

Trace form

24 * q + 4 * q^2 - 8 * q^4 + 16 * q^5 - 24 * q^8 - 12 * q^9 + 4 * q^10 - 4 * q^11 - 16 * q^12 + 4 * q^13 - 4 * q^15 + 8 * q^16 - 20 * q^17 - 8 * q^18 + 8 * q^19 + 20 * q^20 - 4 * q^22 - 8 * q^23 + 40 * q^25 - 20 * q^26 - 12 * q^29 + 16 * q^30 - 8 * q^31 - 12 * q^32 - 4 * q^33 + 32 * q^34 + 4 * q^35 - 8 * q^36 - 8 * q^37 + 56 * q^38 + 8 * q^39 + 16 * q^40 - 16 * q^41 + 4 * q^42 + 28 * q^43 - 48 * q^44 - 8 * q^45 + 20 * q^46 - 48 * q^47 - 12 * q^49 - 4 * q^50 - 24 * q^51 - 20 * q^52 + 16 * q^53 - 12 * q^55 - 32 * q^58 - 12 * q^59 + 56 * q^60 - 24 * q^61 + 44 * q^62 - 88 * q^64 - 20 * q^65 + 32 * q^66 - 20 * q^67 - 28 * q^68 - 4 * q^69 - 48 * q^70 + 12 * q^72 + 16 * q^73 + 20 * q^74 + 16 * q^75 + 40 * q^76 + 16 * q^77 + 24 * q^78 - 40 * q^79 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 112 * q^83 - 4 * q^85 + 80 * q^86 - 8 * q^87 - 12 * q^88 + 48 * q^89 - 8 * q^90 - 8 * q^91 + 40 * q^92 - 24 * q^94 - 4 * q^95 + 40 * q^96 + 4 * q^97 + 4 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.2.k.a	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	\(\Q(\zeta_{18})\)	None		✓			273.2.k.a	$2$	$0$	\(0\)	\(-3\)	\(12\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
273.2.k.b	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	6.0.6040683.1	None		✓			273.2.k.b	$2$	$0$	\(0\)	\(3\)	\(4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{4})q^{3}+(\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
273.2.k.c	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	6.0.64827.1	None		✓			273.2.k.c	$2$	$0$	\(2\)	\(-3\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
273.2.k.d	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	6.0.771147.1	None		✓			273.2.k.d	$2$	$0$	\(2\)	\(3\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)