Space of modular forms of level 91, weight 4, and Character 91.g

• Label: 91.4.g
• Level: $91$
• Weight: $4$
• Character orbit: 91.g
• Rep. character: $\chi_{91}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $37$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	91.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(37\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(91, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	52	52	0
Eisenstein series	8	8	0

Trace form

52 * q + q^2 + 10 * q^3 - 95 * q^4 - 2 * q^5 - 18 * q^6 + q^7 - 24 * q^8 + 362 * q^9 + 110 * q^10 + 42 * q^11 - 96 * q^12 + 82 * q^13 - 140 * q^14 - 83 * q^15 - 339 * q^16 - 133 * q^17 - 39 * q^18 + 414 * q^19 + 66 * q^20 + 97 * q^21 - 172 * q^22 - 95 * q^23 - 128 * q^24 - 484 * q^25 + 208 * q^26 + 94 * q^27 + 498 * q^28 - 184 * q^29 - 332 * q^30 + 116 * q^31 + 167 * q^32 - 1106 * q^33 + 1088 * q^34 - 18 * q^35 - 65 * q^36 + 29 * q^37 - 418 * q^38 + 944 * q^39 - 1242 * q^40 + 394 * q^41 + 1614 * q^42 + 342 * q^43 - 110 * q^44 - 343 * q^45 - 274 * q^46 - 80 * q^47 - 804 * q^48 - 1003 * q^49 - 318 * q^50 + 246 * q^51 - 164 * q^52 + 1228 * q^53 - 417 * q^54 - 559 * q^55 + 2731 * q^56 - 1838 * q^57 - 1786 * q^58 + 753 * q^59 - 395 * q^60 + 4682 * q^61 - 1056 * q^62 - 1576 * q^63 + 3416 * q^64 - 1112 * q^65 - 2821 * q^66 - 3366 * q^67 - 2353 * q^68 - 2296 * q^69 + 2302 * q^70 - 1332 * q^71 + 3742 * q^72 + 980 * q^73 + 1519 * q^74 + 178 * q^75 - 2866 * q^76 - 2483 * q^77 - 2191 * q^78 + 1122 * q^79 + 3616 * q^80 - 1348 * q^81 + 3680 * q^82 + 1468 * q^83 - 3024 * q^84 + 2283 * q^85 - 1960 * q^86 - 4421 * q^87 + 2742 * q^88 - 955 * q^89 + 4644 * q^90 + 2005 * q^91 + 9266 * q^92 + 1509 * q^93 + 4612 * q^94 - 2409 * q^95 - 1638 * q^96 + 380 * q^97 + 1557 * q^98 + 3732 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(91, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.4.g.a	$91$	$4$	91.g	91.g	$3$	$52$	$26$	$5.369$		None		✓	✓	✓	91.4.g.a	$2$	$0$	\(1\)	\(10\)	\(-2\)	\(1\)		$\mathrm{SU}(2)[C_{3}]$