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

• Label: 273.2.l
• Level: $273$
• Weight: $2$
• Character orbit: 273.l
• Rep. character: $\chi_{273}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $38$
• Newform subspaces: $3$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	82	38	44
Cusp forms	66	38	28
Eisenstein series	16	0	16

Trace form

38 * q - 3 * q^3 + 40 * q^4 - 19 * q^9 - 8 * q^10 - 4 * q^11 - 8 * q^12 + 2 * q^13 - 16 * q^14 + 60 * q^16 - 8 * q^17 - 3 * q^19 - 8 * q^20 - 5 * q^21 - 2 * q^22 + 8 * q^23 + 12 * q^24 - 25 * q^25 + 46 * q^26 + 6 * q^27 - 16 * q^28 - 11 * q^31 - 40 * q^32 - 56 * q^34 + 10 * q^35 - 20 * q^36 - 46 * q^37 + 24 * q^38 + 13 * q^39 - 34 * q^40 + 18 * q^41 - 14 * q^42 + 4 * q^43 - 20 * q^44 + 16 * q^46 + 12 * q^47 - 18 * q^48 + 6 * q^49 - 2 * q^50 + 8 * q^51 - 66 * q^52 + 24 * q^53 - 34 * q^55 - 74 * q^56 - 38 * q^57 + 20 * q^58 + 64 * q^59 + 32 * q^60 - 9 * q^61 + 16 * q^62 + 3 * q^63 + 36 * q^64 - 30 * q^65 - 16 * q^66 + 17 * q^67 - 64 * q^68 - 12 * q^69 + 76 * q^70 + 10 * q^71 + 4 * q^73 - 24 * q^74 + 58 * q^75 - 12 * q^76 - 10 * q^77 + 10 * q^78 - 19 * q^79 + 20 * q^80 - 19 * q^81 - 14 * q^82 + 64 * q^83 - 8 * q^84 - 20 * q^85 + 20 * q^86 + 60 * q^87 + 12 * q^88 - 32 * q^89 + 16 * q^90 + 4 * q^91 - 4 * q^92 + 34 * q^93 - 64 * q^94 + 72 * q^95 + 14 * q^96 + 23 * q^97 - 58 * 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.l.a	$273$	$2$	273.l	91.h	$3$	$2$	$1$	$2.180$	\(\Q(\sqrt{-3}) \)	None		✓			273.2.j.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}-2q^{4}+(-3+2\zeta_{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
273.2.l.b	$273$	$2$	273.l	91.h	$3$	$16$	$8$	$2.180$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			273.2.j.b	$2$	$0$	\(0\)	\(8\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.l.c	$273$	$2$	273.l	91.h	$3$	$20$	$10$	$2.180$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		273.2.j.c	$2$	$0$	\(0\)	\(-10\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(-1+\beta _{7})q^{3}+(2+\beta _{2})q^{4}+\cdots\)

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

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