Space of modular forms of level 97, weight 4, and trivial character

• Label: 97.4.a
• Level: $97$
• Weight: $4$
• Character orbit: 97.a
• Rep. character: $\chi_{97}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	97.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(97))\).

	Total	New	Old
Modular forms	26	24	2
Cusp forms	24	24	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.

\(97\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(14\)	\(13\)	\(1\)		\(13\)	\(13\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(12\)	\(11\)	\(1\)		\(11\)	\(11\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

24 * q - 2 * q^2 + 94 * q^4 - 18 * q^5 - 26 * q^6 - 10 * q^7 + 24 * q^8 + 244 * q^9 - 32 * q^10 + 20 * q^11 + 54 * q^12 - 74 * q^13 - 34 * q^14 - 256 * q^15 + 366 * q^16 - 88 * q^17 - 270 * q^18 - 28 * q^19 - 362 * q^20 - 252 * q^21 + 24 * q^22 - 6 * q^23 - 178 * q^24 + 736 * q^25 + 590 * q^26 - 444 * q^27 - 306 * q^28 - 230 * q^29 + 338 * q^30 - 72 * q^31 + 60 * q^32 - 132 * q^33 - 298 * q^34 + 240 * q^35 + 1028 * q^36 + 6 * q^37 - 424 * q^38 - 352 * q^39 + 216 * q^40 - 572 * q^41 - 232 * q^42 - 480 * q^43 + 586 * q^44 - 310 * q^45 + 772 * q^46 - 432 * q^47 + 2728 * q^48 + 604 * q^49 - 864 * q^50 + 1068 * q^51 - 718 * q^52 + 416 * q^53 - 838 * q^54 + 276 * q^55 - 1610 * q^56 + 284 * q^57 - 696 * q^58 + 200 * q^59 - 5052 * q^60 - 1176 * q^61 + 730 * q^62 + 278 * q^63 + 2596 * q^64 + 128 * q^65 + 944 * q^66 - 1140 * q^67 - 4394 * q^68 + 656 * q^69 + 2080 * q^70 + 262 * q^71 - 2892 * q^72 + 228 * q^73 + 4058 * q^74 - 8 * q^75 + 2338 * q^76 + 1996 * q^77 + 1202 * q^78 + 1244 * q^79 - 7504 * q^80 + 2064 * q^81 + 682 * q^82 + 196 * q^83 - 1814 * q^84 - 596 * q^85 + 598 * q^86 + 2172 * q^87 - 190 * q^88 + 824 * q^89 + 612 * q^90 - 556 * q^91 - 2524 * q^92 - 2068 * q^93 + 724 * q^94 + 4180 * q^95 - 5284 * q^96 - 194 * q^97 - 1846 * q^98 - 2032 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(97))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		97
97.4.a.a	$97$	$4$	97.a	1.a	$1$	$11$	$11$	$5.723$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	97.4.a.a	$1$	$1$	\(-11\)	\(-12\)	\(-34\)	\(-68\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{7})q^{3}+(3+\cdots)q^{4}+\cdots\)
97.4.a.b	$97$	$4$	97.a	1.a	$1$	$13$	$13$	$5.723$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓	✓	97.4.a.b	$1$	$0$	\(9\)	\(12\)	\(16\)	\(58\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{6})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots\)