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

• Label: 273.4.e
• Level: $273$
• Weight: $4$
• Character orbit: 273.e
• Rep. character: $\chi_{273}(209,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $149$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	273.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(149\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	116	96	20
Cusp forms	108	96	12
Eisenstein series	8	0	8

Trace form

96 * q - 384 * q^4 - 12 * q^7 - 56 * q^9 + 168 * q^15 + 1776 * q^16 - 140 * q^18 - 64 * q^21 - 528 * q^22 + 2976 * q^25 + 576 * q^28 + 148 * q^30 + 1152 * q^36 - 120 * q^37 - 1386 * q^42 - 1344 * q^43 + 3648 * q^46 + 2100 * q^49 + 2428 * q^51 + 2432 * q^57 - 3264 * q^58 - 1948 * q^60 - 2164 * q^63 - 11088 * q^64 + 1632 * q^67 + 5784 * q^70 + 1336 * q^72 + 1820 * q^78 - 1992 * q^79 - 3736 * q^81 + 840 * q^84 - 6000 * q^85 - 96 * q^88 + 312 * q^91 - 736 * q^93 + 4712 * 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.e.a	$273$	$4$	273.e	21.c	$2$	$96$	$96$	$16.108$		None		✓	✓	✓	273.4.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{2}]$

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

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