Space of modular forms of level 197, weight 12, and trivial character

• Label: 197.12.a
• Level: $197$
• Weight: $12$
• Character orbit: 197.a
• Rep. character: $\chi_{197}(1,\cdot)$
• Character field: $\Q$
• Dimension: $179$
• Newform subspaces: $2$
• Sturm bound: $198$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$197$
Weight:	$k$	$=$	$12$
Character orbit:	$[\chi]$	$=$	197.a (trivial)
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$198$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{12}(\Gamma_0(197))$.

	Total	New	Old
Modular forms	183	179	4
Cusp forms	181	179	2
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
$+$	$92$
$-$	$87$

Trace form

179 * q - 32 * q^2 - 506 * q^3 + 181248 * q^4 - 4292 * q^5 + 15552 * q^6 + 73958 * q^7 - 23466 * q^8 + 10915153 * q^9 - 451446 * q^10 - 1707062 * q^11 - 1036288 * q^12 + 3046244 * q^13 + 3377650 * q^14 - 4726682 * q^15 + 181403648 * q^16 - 138632 * q^17 - 16589758 * q^18 + 4338482 * q^19 + 44409558 * q^20 + 46136452 * q^21 + 44896562 * q^22 - 77277104 * q^23 - 30847446 * q^24 + 1738156885 * q^25 - 62733812 * q^26 + 67920886 * q^27 + 49491820 * q^28 - 251788870 * q^29 - 474827530 * q^30 + 161802396 * q^31 + 272554840 * q^32 + 78935140 * q^33 - 144713724 * q^34 + 215781724 * q^35 + 10506506996 * q^36 - 142573880 * q^37 - 857822124 * q^38 + 2394560438 * q^39 - 1799514708 * q^40 - 2377153492 * q^41 + 1614214262 * q^42 + 880054814 * q^43 + 101369540 * q^44 + 4773894 * q^45 + 451010202 * q^46 - 5301347590 * q^47 + 8809371172 * q^48 + 50524045501 * q^49 - 10601888772 * q^50 - 3162536174 * q^51 + 18317913802 * q^52 + 119766580 * q^53 - 4972778874 * q^54 + 9434182794 * q^55 + 35328186936 * q^56 - 10571741984 * q^57 - 4007942798 * q^58 + 16187715582 * q^59 + 6009852298 * q^60 - 14465398644 * q^61 - 43463472262 * q^62 + 15168448702 * q^63 + 162486953526 * q^64 + 2232825030 * q^65 - 19819831838 * q^66 + 47254686328 * q^67 + 25121875156 * q^68 - 74474183392 * q^69 + 24041413558 * q^70 + 14752009558 * q^71 + 84397626210 * q^72 - 34758371608 * q^73 - 95262925132 * q^74 + 6656822788 * q^75 + 55547915476 * q^76 - 1898299652 * q^77 + 31518277918 * q^78 + 29767846366 * q^79 + 115197283696 * q^80 + 635447630747 * q^81 + 70344065848 * q^82 + 164969853872 * q^83 + 147596010202 * q^84 - 8103076680 * q^85 + 197759629654 * q^86 + 99578816480 * q^87 + 265449026946 * q^88 + 53135278642 * q^89 - 478903734130 * q^90 - 37783882660 * q^91 - 421620319388 * q^92 + 269832424126 * q^93 - 246616469772 * q^94 - 45076718962 * q^95 - 167130334250 * q^96 - 12329623248 * q^97 - 23184330508 * q^98 - 228362184182 * q^99

Decomposition of $S_{12}^{\mathrm{new}}(\Gamma_0(197))$ 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
197.12.a.a	$197$	$12$	197.a	1.a	$1$	$87$	$87$	$151.364$		None	✓	✓	✓	✓	197.12.a.a	$1$	$1$	$-96$	$-2926$	$-20896$	$-231933$		$-$	$-$		$\mathrm{SU}(2)$
197.12.a.b	$197$	$12$	197.a	1.a	$1$	$92$	$92$	$151.364$		None	✓	✓	✓	✓	197.12.a.b	$1$	$0$	$64$	$2420$	$16604$	$305891$		$+$	$+$		$\mathrm{SU}(2)$

Decomposition of $S_{12}^{\mathrm{old}}(\Gamma_0(197))$ into lower level spaces

$S_{12}^{\mathrm{old}}(\Gamma_0(197)) \simeq$ $S_{12}^{\mathrm{new}}(\Gamma_0(1))$$^{\oplus 2}$