Space of modular forms of level 197, weight 2, and trivial character

• Label: 197.2.a
• Level: $197$
• Weight: $2$
• Character orbit: 197.a
• Rep. character: $\chi_{197}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $33$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(33\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(197))\).

	Total	New	Old
Modular forms	17	17	0
Cusp forms	16	16	0
Eisenstein series	1	1	0

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
\(+\)		\(6\)	\(6\)	\(0\)		\(6\)	\(6\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(11\)	\(11\)	\(0\)		\(10\)	\(10\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

16 * q - 2 * q^2 + 2 * q^3 + 12 * q^4 - 2 * q^5 - 6 * q^6 - 2 * q^7 - 6 * q^8 + 22 * q^9 - 12 * q^10 - 2 * q^11 - 8 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^15 - 8 * q^16 - 2 * q^17 - 4 * q^18 - 2 * q^19 + 2 * q^20 + 12 * q^21 + 4 * q^22 - 8 * q^23 + 8 * q^25 + 2 * q^26 - 10 * q^27 + 8 * q^28 + 18 * q^30 + 12 * q^31 - 4 * q^32 - 4 * q^33 - 12 * q^34 - 4 * q^35 + 22 * q^36 + 2 * q^37 - 4 * q^38 + 14 * q^39 - 18 * q^40 - 14 * q^41 - 2 * q^42 - 14 * q^43 - 12 * q^45 + 6 * q^46 + 10 * q^47 - 8 * q^48 + 14 * q^49 - 2 * q^50 - 14 * q^51 + 2 * q^52 + 6 * q^53 - 6 * q^54 - 30 * q^55 - 16 * q^56 + 16 * q^57 - 34 * q^58 - 14 * q^59 - 18 * q^60 + 6 * q^61 - 18 * q^62 - 42 * q^63 - 42 * q^64 - 26 * q^65 + 14 * q^66 - 4 * q^67 + 4 * q^68 + 38 * q^70 - 2 * q^71 - 6 * q^72 + 22 * q^73 + 12 * q^74 + 32 * q^75 + 38 * q^76 + 4 * q^77 - 46 * q^78 + 14 * q^79 + 20 * q^80 + 80 * q^81 + 68 * q^82 + 4 * q^83 + 18 * q^84 - 36 * q^85 + 2 * q^86 + 8 * q^87 - 4 * q^89 - 88 * q^90 + 28 * q^91 + 4 * q^92 + 26 * q^93 + 24 * q^94 + 22 * q^95 + 56 * q^96 - 42 * q^97 + 42 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(197))\) 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
197.2.a.a	$197$	$2$	197.a	1.a	$1$	$1$	$1$	$1.573$	\(\Q\)	None	✓	✓			197.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{7}-3q^{9}+4q^{11}+\cdots\)
197.2.a.b	$197$	$2$	197.a	1.a	$1$	$5$	$5$	$1.573$	5.5.24217.1	None	✓	✓	✓		197.2.a.b	$1$	$1$	\(0\)	\(-8\)	\(-4\)	\(-10\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
197.2.a.c	$197$	$2$	197.a	1.a	$1$	$10$	$10$	$1.573$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	197.2.a.c	$1$	$0$	\(0\)	\(10\)	\(2\)	\(11\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)