Space of modular forms of level 538, weight 2, and Character 538.e

• Label: 538.2.e
• Level: $538$
• Weight: $2$
• Character orbit: 538.e
• Rep. character: $\chi_{538}(9,\cdot)$
• Character field: $\Q(\zeta_{134})$
• Dimension: $1452$
• Newform subspaces: $1$
• Sturm bound: $135$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\) and degree \(66\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 269 \)
Character field:			\(\Q(\zeta_{134})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(135\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(538, [\chi])\).

	Total	New	Old
Modular forms	4620	1452	3168
Cusp forms	4356	1452	2904
Eisenstein series	264	0	264

Trace form

1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(538, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
538.2.e.a	$538$	$2$	538.e	269.e	$134$	$1452$	$22$	$4.296$		None		✓	✓	✓	538.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{134}]$

Decomposition of \(S_{2}^{\mathrm{old}}(538, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(538, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(269, [\chi])\)\(^{\oplus 2}\)