Space of modular forms of level 197, weight 10, and trivial character

• Label: 197.10.a
• Level: $197$
• Weight: $10$
• Character orbit: 197.a
• Rep. character: $\chi_{197}(1,\cdot)$
• Character field: $\Q$
• Dimension: $147$
• Newform subspaces: $2$
• Sturm bound: $165$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(165\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(197))\).

	Total	New	Old
Modular forms	149	147	2
Cusp forms	147	147	0
Eisenstein series	2	0	2

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

\(197\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(72\)	\(71\)	\(1\)		\(71\)	\(71\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(77\)	\(76\)	\(1\)		\(76\)	\(76\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

147 * q + 16 * q^2 - 2 * q^3 + 37632 * q^4 + 2842 * q^5 - 7584 * q^6 + 1140 * q^7 + 11574 * q^8 + 938221 * q^9 - 17814 * q^10 - 22610 * q^11 - 80896 * q^12 + 46310 * q^13 + 200706 * q^14 - 125252 * q^15 + 9633792 * q^16 + 715870 * q^17 + 343490 * q^18 - 1103338 * q^19 + 715478 * q^20 - 1333544 * q^21 - 1317886 * q^22 + 3562216 * q^23 - 5954214 * q^24 + 54489163 * q^25 - 814756 * q^26 + 2006164 * q^27 - 7390148 * q^28 + 5286264 * q^29 + 15382166 * q^30 + 594442 * q^31 - 2985496 * q^32 + 4918636 * q^33 + 195588 * q^34 - 9474028 * q^35 + 227278196 * q^36 - 547708 * q^37 + 53847140 * q^38 - 78661768 * q^39 + 60029532 * q^40 - 26533502 * q^41 + 52412006 * q^42 + 66230854 * q^43 - 51186588 * q^44 + 163977798 * q^45 + 108966362 * q^46 - 76738004 * q^47 - 154639484 * q^48 + 808307735 * q^49 + 94332844 * q^50 + 75470668 * q^51 - 77679798 * q^52 - 46332360 * q^53 + 40122246 * q^54 + 24319316 * q^55 - 117568648 * q^56 + 224193340 * q^57 + 283520674 * q^58 - 100982534 * q^59 - 266068694 * q^60 - 406109492 * q^61 - 86160438 * q^62 + 38236984 * q^63 + 2547350454 * q^64 - 445900280 * q^65 - 77274062 * q^66 + 175962902 * q^67 + 893282020 * q^68 + 799861844 * q^69 + 735836806 * q^70 + 860565838 * q^71 + 172789938 * q^72 + 524963490 * q^73 - 359189628 * q^74 + 457123558 * q^75 - 1875594332 * q^76 - 448513976 * q^77 - 2709389474 * q^78 + 617151738 * q^79 + 407235440 * q^80 + 5368673387 * q^81 - 1620121960 * q^82 - 884548118 * q^83 + 351927418 * q^84 - 1876479824 * q^85 - 1895528074 * q^86 - 376250512 * q^87 - 2390972670 * q^88 - 1910470810 * q^89 - 665483074 * q^90 - 2169473720 * q^91 + 3915451492 * q^92 - 1294333208 * q^93 - 2456364092 * q^94 - 3259036424 * q^95 - 2016254858 * q^96 + 154080246 * q^97 - 690396732 * q^98 + 2350789054 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(197))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		197
197.10.a.a	$197$	$10$	197.a	1.a	$1$	$71$	$71$	$101.462$		None	✓	✓	✓	✓	197.10.a.a	$1$	$1$	\(-32\)	\(-892\)	\(-2329\)	\(-37846\)		$+$	$+$		$\mathrm{SU}(2)$
197.10.a.b	$197$	$10$	197.a	1.a	$1$	$76$	$76$	$101.462$		None	✓	✓	✓	✓	197.10.a.b	$1$	$0$	\(48\)	\(890\)	\(5171\)	\(38986\)		$-$	$-$		$\mathrm{SU}(2)$