Space of modular forms of level 667, weight 6, and trivial character

• Label: 667.6.a
• Level: $667$
• Weight: $6$
• Character orbit: 667.a
• Rep. character: $\chi_{667}(1,\cdot)$
• Character field: $\Q$
• Dimension: $258$
• Newform subspaces: $4$
• Sturm bound: $360$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$667 = 23 \cdot 29$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	667.a (trivial)
Character field:			$\Q$
Newform subspaces:			$4$
Sturm bound:			$360$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(\Gamma_0(667))$.

	Total	New	Old
Modular forms	302	258	44
Cusp forms	298	258	40
Eisenstein series	4	0	4

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

$23$	$29$	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
$+$	$+$	$+$		$72$	$64$	$8$		$71$	$64$	$7$		$1$	$0$	$1$
$+$	$-$	$-$		$76$	$65$	$11$		$75$	$65$	$10$		$1$	$0$	$1$
$-$	$+$	$-$		$79$	$68$	$11$		$78$	$68$	$10$		$1$	$0$	$1$
$-$	$-$	$+$		$75$	$61$	$14$		$74$	$61$	$13$		$1$	$0$	$1$
Plus space		$+$		$147$	$125$	$22$		$145$	$125$	$20$		$2$	$0$	$2$
Minus space		$-$		$155$	$133$	$22$		$153$	$133$	$20$		$2$	$0$	$2$

Trace form

258 * q - 8 * q^2 + 8 * q^3 + 4192 * q^4 - 16 * q^6 - 188 * q^7 - 876 * q^8 + 21354 * q^9 - 68 * q^10 - 916 * q^11 - 212 * q^12 - 300 * q^13 + 2288 * q^14 + 75744 * q^16 + 3012 * q^17 + 2220 * q^18 - 8784 * q^19 + 9268 * q^20 + 4968 * q^21 + 4348 * q^22 - 6016 * q^24 + 166250 * q^25 + 2048 * q^26 - 21592 * q^27 - 14200 * q^28 - 5046 * q^29 - 11832 * q^30 - 396 * q^31 - 54480 * q^32 - 51072 * q^33 + 34944 * q^34 + 27772 * q^35 + 447416 * q^36 - 29092 * q^37 - 18560 * q^38 - 29708 * q^39 - 29712 * q^40 + 7496 * q^41 + 91816 * q^42 + 53056 * q^43 + 59212 * q^44 + 70136 * q^45 - 8464 * q^46 + 10552 * q^47 - 4736 * q^48 + 559334 * q^49 + 68508 * q^50 - 51840 * q^51 - 688 * q^52 + 48692 * q^53 - 151540 * q^54 + 55148 * q^55 - 75144 * q^56 + 189648 * q^57 - 6728 * q^58 + 8372 * q^59 + 156960 * q^60 - 139412 * q^61 + 160532 * q^62 + 194904 * q^63 + 1242664 * q^64 + 8080 * q^65 + 231016 * q^66 - 43352 * q^67 - 269056 * q^68 - 38088 * q^69 - 654280 * q^70 + 145540 * q^71 - 110660 * q^72 + 44064 * q^73 + 288296 * q^74 + 306444 * q^75 - 472076 * q^76 + 55916 * q^77 - 625560 * q^78 - 199760 * q^79 - 245156 * q^80 + 1810290 * q^81 - 164996 * q^82 + 271080 * q^83 + 146632 * q^84 + 71956 * q^85 - 10648 * q^86 - 90828 * q^87 + 53120 * q^88 - 256752 * q^89 + 368424 * q^90 + 198368 * q^91 - 254420 * q^93 - 90324 * q^94 + 222248 * q^95 + 109352 * q^96 + 499264 * q^97 + 397464 * q^98 - 897052 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(\Gamma_0(667))$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		23	29
667.6.a.a	$667$	$6$	667.a	1.a	$1$	$61$	$61$	$106.976$		None	✓	✓	✓	✓	667.6.a.a	$1$	$1$	$-24$	$-97$	$-400$	$-243$		$-$	$-$	$+$		$\mathrm{SU}(2)$
667.6.a.b	$667$	$6$	667.a	1.a	$1$	$64$	$64$	$106.976$		None	✓	✓	✓	✓	667.6.a.b	$1$	$1$	$-12$	$-7$	$-400$	$-243$		$+$	$+$	$+$		$\mathrm{SU}(2)$
667.6.a.c	$667$	$6$	667.a	1.a	$1$	$65$	$65$	$106.976$		None	✓	✓	✓	✓	667.6.a.c	$1$	$0$	$16$	$47$	$400$	$149$		$+$	$-$	$-$		$\mathrm{SU}(2)$
667.6.a.d	$667$	$6$	667.a	1.a	$1$	$68$	$68$	$106.976$		None	✓	✓	✓	✓	667.6.a.d	$1$	$0$	$12$	$65$	$400$	$149$		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{6}^{\mathrm{old}}(\Gamma_0(667))$ into lower level spaces

$S_{6}^{\mathrm{old}}(\Gamma_0(667)) \simeq$ $S_{6}^{\mathrm{new}}(\Gamma_0(23))$$^{\oplus 2}$$\oplus$$S_{6}^{\mathrm{new}}(\Gamma_0(29))$$^{\oplus 2}$