Space of modular forms of level 197, weight 14, and trivial character

• Label: 197.14.a
• Level: $197$
• Weight: $14$
• Character orbit: 197.a
• Rep. character: $\chi_{197}(1,\cdot)$
• Character field: $\Q$
• Dimension: $213$
• Newform subspaces: $2$
• Sturm bound: $231$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(231\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(197))\).

	Total	New	Old
Modular forms	215	213	2
Cusp forms	213	213	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.

\(197\)	Dim
\(+\)	\(104\)
\(-\)	\(109\)

Trace form

213 * q + 64 * q^2 - 2 * q^3 + 880640 * q^4 - 10508 * q^5 + 299904 * q^6 - 403306 * q^7 - 290442 * q^8 + 111071167 * q^9 + 6747306 * q^10 + 10510498 * q^11 - 4931584 * q^12 - 35067412 * q^13 - 14577374 * q^14 - 98882522 * q^15 + 3674210304 * q^16 + 118781464 * q^17 - 49010926 * q^18 - 355966726 * q^19 - 84061482 * q^20 - 292293140 * q^21 - 1081805054 * q^22 - 1712247728 * q^23 + 5351789946 * q^24 + 53938480123 * q^25 - 596088644 * q^26 + 1557918478 * q^27 + 2275553820 * q^28 + 7232993390 * q^29 - 7563496234 * q^30 + 3700964284 * q^31 - 20911534520 * q^32 - 22743610820 * q^33 - 1550192412 * q^34 - 961430228 * q^35 + 477982208372 * q^36 - 10895743560 * q^37 + 33184592772 * q^38 + 5453286662 * q^39 + 18881742972 * q^40 + 43276377284 * q^41 - 80174787514 * q^42 - 10620751642 * q^43 - 133504177372 * q^44 + 16660153458 * q^45 - 57910920102 * q^46 + 99590810330 * q^47 - 251835700796 * q^48 + 2850374555771 * q^49 + 164291940924 * q^50 - 262674261398 * q^51 - 234926037174 * q^52 + 504468579580 * q^53 + 1081242585222 * q^54 - 498675903174 * q^55 - 980368023816 * q^56 + 238688003488 * q^57 + 55490658914 * q^58 + 51914853510 * q^59 - 2304732128534 * q^60 + 951426418852 * q^61 + 2618909324714 * q^62 - 2560924922306 * q^63 + 16282595907254 * q^64 - 37148268870 * q^65 + 7860885141778 * q^66 + 724667994024 * q^67 - 171108760508 * q^68 + 3136464958304 * q^69 - 2804901282394 * q^70 - 1188579531482 * q^71 - 8726729616750 * q^72 + 2111345205224 * q^73 + 5821521205124 * q^74 - 7712925574172 * q^75 - 4971403165308 * q^76 - 3142226117036 * q^77 - 1560438154274 * q^78 - 1389457688898 * q^79 - 1564512175760 * q^80 + 54216024955229 * q^81 + 5833702556024 * q^82 - 5264184894976 * q^83 + 3017684123962 * q^84 + 9639901623336 * q^85 + 9750267489142 * q^86 + 11707978292000 * q^87 - 17835580413438 * q^88 + 6643190964430 * q^89 + 30548206924766 * q^90 + 24490130487180 * q^91 - 38647820050844 * q^92 - 15026998386278 * q^93 + 33691305982308 * q^94 + 12042669661646 * q^95 + 50450362127926 * q^96 + 3670692673696 * q^97 - 15983307150796 * q^98 + 3417936671410 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(197))\) 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
197.14.a.a	$197$	$14$	197.a	1.a	$1$	$104$	$104$	$211.245$		None	✓	✓	✓	✓	197.14.a.a	$1$	$1$	\(-128\)	\(-8020\)	\(-99004\)	\(-2084037\)		$+$	$+$		$\mathrm{SU}(2)$
197.14.a.b	$197$	$14$	197.a	1.a	$1$	$109$	$109$	$211.245$		None	✓	✓	✓	✓	197.14.a.b	$1$	$0$	\(192\)	\(8018\)	\(88496\)	\(1680731\)		$-$	$-$		$\mathrm{SU}(2)$