Space of modular forms of level 392, weight 3, and Character 392.s

• Label: 392.3.s
• Level: $392$
• Weight: $3$
• Character orbit: 392.s
• Rep. character: $\chi_{392}(43,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $660$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.s (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 392 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(392, [\chi])\).

	Total	New	Old
Modular forms	684	684	0
Cusp forms	660	660	0
Eisenstein series	24	24	0

Trace form

660 * q - 5 * q^2 - 10 * q^3 - 5 * q^4 + 3 * q^6 + q^8 - 328 * q^9 + 5 * q^10 - 10 * q^11 + 38 * q^12 + 91 * q^14 + 19 * q^16 - 10 * q^17 - 36 * q^18 - 24 * q^19 + 45 * q^20 - 9 * q^22 - 147 * q^24 + 500 * q^25 - 59 * q^26 + 26 * q^27 - 252 * q^28 - 100 * q^30 + 35 * q^32 + 26 * q^33 - 61 * q^34 - 14 * q^35 + 25 * q^36 - 81 * q^38 + 245 * q^40 - 10 * q^41 + 63 * q^42 - 10 * q^43 + 181 * q^44 - 3 * q^46 - 100 * q^48 - 28 * q^49 - 240 * q^50 + 186 * q^51 - 83 * q^52 + 286 * q^54 - 588 * q^56 - 196 * q^57 + 205 * q^58 - 138 * q^59 - 599 * q^60 + 13 * q^62 - 227 * q^64 - 110 * q^65 + 105 * q^66 - 312 * q^67 + 376 * q^68 + 679 * q^70 + 158 * q^72 + 150 * q^73 + 129 * q^74 - 74 * q^75 - 418 * q^76 - 575 * q^78 - 516 * q^80 - 740 * q^81 + 842 * q^82 - 490 * q^83 - 1106 * q^84 + 137 * q^86 - 471 * q^88 - 106 * q^89 + 912 * q^90 + 658 * q^91 - 536 * q^92 - 766 * q^94 - 106 * q^96 + 232 * q^97 - 301 * q^98 + 336 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(392, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
392.3.s.a	$392$	$3$	392.s	392.s	$14$	$660$	$110$	$10.681$		None		✓	✓	✓	392.3.s.a	$4$	$0$	\(-5\)	\(-10\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$