Space of modular forms of level 99, weight 4, and Character 99.g

• Label: 99.4.g
• Level: $99$
• Weight: $4$
• Character orbit: 99.g
• Rep. character: $\chi_{99}(32,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(99, [\chi])\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	68	68	0
Eisenstein series	8	8	0

Trace form

68 * q - 4 * q^3 - 130 * q^4 - 18 * q^5 - 82 * q^9 - 66 * q^11 + 146 * q^12 - 6 * q^14 - 170 * q^15 - 466 * q^16 + 234 * q^20 - 3 * q^22 - 258 * q^23 + 720 * q^25 + 884 * q^27 - 20 * q^31 + 158 * q^33 + 162 * q^34 - 1048 * q^36 - 80 * q^37 - 1536 * q^38 + 1938 * q^42 + 328 * q^45 + 1158 * q^47 - 2536 * q^48 + 1076 * q^49 - 866 * q^55 + 1932 * q^56 + 534 * q^58 + 1026 * q^59 - 2186 * q^60 + 2840 * q^64 + 1308 * q^66 - 470 * q^67 - 3176 * q^69 + 96 * q^70 + 1356 * q^75 - 2835 * q^77 + 522 * q^78 + 2054 * q^81 + 2112 * q^82 - 1242 * q^86 + 435 * q^88 - 2388 * q^91 - 9378 * q^92 - 4922 * q^93 - 524 * q^97 + 491 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(99, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.4.g.a	$99$	$4$	99.g	99.g	$6$	$4$	$2$	$5.841$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		✓			99.4.g.a	$4$	$0$	\(0\)	\(8\)	\(54\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+(4\beta _{2}-\beta _{3})q^{3}+8\beta _{2}q^{4}+(18-9\beta _{2}+\cdots)q^{5}+\cdots\)
99.4.g.b	$99$	$4$	99.g	99.g	$6$	$64$	$32$	$5.841$		None		✓	✓		99.4.g.b	$4$	$0$	\(0\)	\(-12\)	\(-72\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$