Space of modular forms of level 4767, weight 2, and trivial character

• Label: 4767.2.a
• Level: $4767$
• Weight: $2$
• Character orbit: 4767.a
• Rep. character: $\chi_{4767}(1,\cdot)$
• Character field: $\Q$
• Dimension: $227$
• Newform subspaces: $8$
• Sturm bound: $1216$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$4767 = 3 \cdot 7 \cdot 227$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4767.a (trivial)
Character field:			$\Q$
Newform subspaces:			$8$
Sturm bound:			$1216$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(4767))$.

	Total	New	Old
Modular forms	612	227	385
Cusp forms	605	227	378
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$3$	$7$	$227$	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
$+$	$+$	$+$	$+$		$61$	$27$	$34$		$61$	$27$	$34$		$0$	$0$	$0$
$+$	$+$	$-$	$-$		$92$	$30$	$62$		$91$	$30$	$61$		$1$	$0$	$1$
$+$	$-$	$+$	$-$		$82$	$35$	$47$		$81$	$35$	$46$		$1$	$0$	$1$
$+$	$-$	$-$	$+$		$71$	$22$	$49$		$70$	$22$	$48$		$1$	$0$	$1$
$-$	$+$	$+$	$-$		$69$	$29$	$40$		$68$	$29$	$39$		$1$	$0$	$1$
$-$	$+$	$-$	$+$		$84$	$26$	$58$		$83$	$26$	$57$		$1$	$0$	$1$
$-$	$-$	$+$	$+$		$74$	$23$	$51$		$73$	$23$	$50$		$1$	$0$	$1$
$-$	$-$	$-$	$-$		$79$	$35$	$44$		$78$	$35$	$43$		$1$	$0$	$1$
Plus space			$+$		$290$	$98$	$192$		$287$	$98$	$189$		$3$	$0$	$3$
Minus space			$-$		$322$	$129$	$193$		$318$	$129$	$189$		$4$	$0$	$4$

Trace form

227 * q + 5 * q^2 - q^3 + 229 * q^4 + 10 * q^5 - 3 * q^6 + 3 * q^7 + 9 * q^8 + 227 * q^9 - 10 * q^10 + 4 * q^11 - 7 * q^12 + 10 * q^13 + q^14 - 6 * q^15 + 221 * q^16 + 22 * q^17 + 5 * q^18 - 20 * q^19 + 38 * q^20 + 3 * q^21 + 20 * q^22 - 8 * q^23 - 15 * q^24 + 245 * q^25 + 22 * q^26 - q^27 + 5 * q^28 + 18 * q^29 - 2 * q^30 - 8 * q^31 + 33 * q^32 - 12 * q^33 - 14 * q^34 - 6 * q^35 + 229 * q^36 + 2 * q^37 - 60 * q^38 + 2 * q^39 - 26 * q^40 + 14 * q^41 - 3 * q^42 - 20 * q^43 - 4 * q^44 + 10 * q^45 - 16 * q^46 - 16 * q^47 - 31 * q^48 + 227 * q^49 + 3 * q^50 - 18 * q^51 - 26 * q^52 - 14 * q^53 - 3 * q^54 - 40 * q^55 + 21 * q^56 + 12 * q^57 - 34 * q^58 - 28 * q^59 - 18 * q^60 + 2 * q^61 - 56 * q^62 + 3 * q^63 + 205 * q^64 + 12 * q^65 - 4 * q^66 - 28 * q^67 - 22 * q^68 - 16 * q^69 + 22 * q^70 - 48 * q^71 + 9 * q^72 + 30 * q^73 - 42 * q^74 + q^75 - 60 * q^76 + 4 * q^77 + 30 * q^78 + 72 * q^79 + 62 * q^80 + 227 * q^81 + 34 * q^82 + 28 * q^83 + 5 * q^84 + 28 * q^85 + 28 * q^86 - 6 * q^87 + 12 * q^88 + 46 * q^89 - 10 * q^90 - 14 * q^91 + 8 * q^92 + 24 * q^93 - 80 * q^94 - 23 * q^96 - 34 * q^97 + 5 * q^98 + 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(4767))$ 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	227
4767.2.a.a	$4767$	$2$	4767.a	1.a	$1$	$22$	$22$	$38.065$		None	✓	✓	✓	✓	4767.2.a.a	$1$	$1$	$-4$	$-22$	$8$	$22$		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
4767.2.a.b	$4767$	$2$	4767.a	1.a	$1$	$23$	$23$	$38.065$		None	✓	✓	✓	✓	4767.2.a.b	$1$	$1$	$-9$	$23$	$-20$	$23$		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
4767.2.a.c	$4767$	$2$	4767.a	1.a	$1$	$26$	$26$	$38.065$		None	✓	✓	✓	✓	4767.2.a.c	$1$	$1$	$-4$	$26$	$-2$	$-26$		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
4767.2.a.d	$4767$	$2$	4767.a	1.a	$1$	$27$	$27$	$38.065$		None	✓	✓	✓	✓	4767.2.a.d	$1$	$1$	$1$	$-27$	$-10$	$-27$		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
4767.2.a.e	$4767$	$2$	4767.a	1.a	$1$	$29$	$29$	$38.065$		None	✓	✓	✓	✓	4767.2.a.e	$1$	$0$	$5$	$29$	$6$	$-29$		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
4767.2.a.f	$4767$	$2$	4767.a	1.a	$1$	$30$	$30$	$38.065$		None	✓	✓	✓	✓	4767.2.a.f	$1$	$0$	$0$	$-30$	$14$	$-30$		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4767.2.a.g	$4767$	$2$	4767.a	1.a	$1$	$35$	$35$	$38.065$		None	✓	✓	✓	✓	4767.2.a.g	$1$	$0$	$7$	$-35$	$-4$	$35$		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4767.2.a.h	$4767$	$2$	4767.a	1.a	$1$	$35$	$35$	$38.065$		None	✓	✓	✓	✓	4767.2.a.h	$1$	$0$	$9$	$35$	$18$	$35$		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(4767))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(4767)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(227))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(681))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1589))$$^{\oplus 2}$