Space of modular forms of level 231, weight 4, and Character 231.u

• Label: 231.4.u
• Level: $231$
• Weight: $4$
• Character orbit: 231.u
• Rep. character: $\chi_{231}(20,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $368$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 231 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(231, [\chi])\).

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

368 * q + 340 * q^4 - 18 * q^7 + 42 * q^9 + 42 * q^15 - 1116 * q^16 - 262 * q^18 - 222 * q^21 + 696 * q^22 - 1516 * q^25 + 38 * q^28 + 624 * q^30 + 1430 * q^36 + 36 * q^37 + 390 * q^39 + 2130 * q^42 - 1376 * q^43 + 1716 * q^46 + 474 * q^49 + 782 * q^51 + 670 * q^57 + 5576 * q^58 - 2708 * q^60 - 739 * q^63 + 5256 * q^64 - 2432 * q^67 + 2280 * q^70 - 3706 * q^72 - 10900 * q^78 + 732 * q^79 - 262 * q^81 - 510 * q^84 + 8008 * q^85 - 832 * q^88 - 5446 * q^91 + 2510 * q^93 - 6218 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(231, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.4.u.a	$231$	$4$	231.u	231.u	$10$	$368$	$92$	$13.629$		None		✓	✓	✓	231.4.u.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-18\)		$\mathrm{SU}(2)[C_{10}]$