Space of modular forms of level 273, weight 4, and Character 273.i

• Label: 273.4.i
• Level: $273$
• Weight: $4$
• Character orbit: 273.i
• Rep. character: $\chi_{273}(79,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $149$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	273.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(149\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(273, [\chi])\).

	Total	New	Old
Modular forms	232	96	136
Cusp forms	216	96	120
Eisenstein series	16	0	16

Trace form

96 * q - 4 * q^2 - 172 * q^4 + 16 * q^5 + 48 * q^6 - 4 * q^7 - 240 * q^8 - 432 * q^9 - 12 * q^10 - 16 * q^11 + 104 * q^13 + 92 * q^14 + 168 * q^15 - 668 * q^16 + 260 * q^17 - 36 * q^18 - 304 * q^19 - 1904 * q^20 + 240 * q^22 + 352 * q^23 - 288 * q^24 - 1308 * q^25 + 1100 * q^28 + 664 * q^29 + 384 * q^30 - 844 * q^31 + 1316 * q^32 - 300 * q^33 + 320 * q^34 - 1616 * q^35 + 3096 * q^36 + 368 * q^37 - 892 * q^38 + 96 * q^40 - 256 * q^41 + 504 * q^42 - 2480 * q^43 - 1280 * q^44 + 144 * q^45 - 304 * q^46 - 528 * q^47 + 1056 * q^48 + 976 * q^49 + 4704 * q^50 + 168 * q^51 - 624 * q^52 + 1836 * q^53 - 216 * q^54 + 40 * q^55 + 3656 * q^56 - 1392 * q^57 + 1308 * q^58 - 1312 * q^59 - 1008 * q^60 - 452 * q^61 - 4216 * q^62 + 288 * q^63 + 4432 * q^64 + 416 * q^65 + 1368 * q^66 - 2368 * q^67 + 6028 * q^68 + 1296 * q^69 - 3300 * q^70 + 752 * q^71 + 1080 * q^72 + 1592 * q^73 + 4524 * q^74 + 7728 * q^76 + 120 * q^77 + 364 * q^79 + 2892 * q^80 - 3888 * q^81 + 3712 * q^82 - 3088 * q^83 - 6384 * q^84 + 144 * q^85 - 4108 * q^86 - 948 * q^87 - 4548 * q^88 - 1200 * q^89 + 216 * q^90 - 624 * q^91 + 1216 * q^92 - 1368 * q^93 - 3728 * q^94 - 5336 * q^95 - 2688 * q^96 + 56 * q^97 + 1248 * q^98 + 288 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(273, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.4.i.a	$273$	$4$	273.i	7.c	$3$	$2$	$1$	$16.108$	\(\Q(\sqrt{-3}) \)	None		✓			273.4.i.a	$2$	$0$	\(5\)	\(-3\)	\(3\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+5\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-17+\cdots)q^{4}+\cdots\)
273.4.i.b	$273$	$4$	273.i	7.c	$3$	$6$	$3$	$16.108$	6.0.432216027.2	None		✓			273.4.i.b	$2$	$0$	\(0\)	\(-9\)	\(27\)	\(38\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-3+3\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
273.4.i.c	$273$	$4$	273.i	7.c	$3$	$14$	$7$	$16.108$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			273.4.i.c	$2$	$0$	\(-8\)	\(-21\)	\(-21\)	\(-34\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}+\beta _{2}+\beta _{4})q^{2}-3\beta _{4}q^{3}+\cdots\)
273.4.i.d	$273$	$4$	273.i	7.c	$3$	$22$	$11$	$16.108$		None		✓			273.4.i.d	$2$	$0$	\(1\)	\(33\)	\(-17\)	\(11\)		$\mathrm{SU}(2)[C_{3}]$
273.4.i.e	$273$	$4$	273.i	7.c	$3$	$26$	$13$	$16.108$		None		✓			273.4.i.e	$2$	$0$	\(-3\)	\(-39\)	\(-15\)	\(-13\)		$\mathrm{SU}(2)[C_{3}]$
273.4.i.f	$273$	$4$	273.i	7.c	$3$	$26$	$13$	$16.108$		None		✓			273.4.i.f	$2$	$0$	\(1\)	\(39\)	\(39\)	\(-13\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(273, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)