Space of modular forms of level 973, weight 2, and trivial character

• Label: 973.2.a
• Level: $973$
• Weight: $2$
• Character orbit: 973.a
• Rep. character: $\chi_{973}(1,\cdot)$
• Character field: $\Q$
• Dimension: $69$
• Newform subspaces: $9$
• Sturm bound: $186$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 973 = 7 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	973.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(186\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(973))\).

	Total	New	Old
Modular forms	94	69	25
Cusp forms	91	69	22
Eisenstein series	3	0	3

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

\(7\)	\(139\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(19\)	\(16\)	\(3\)		\(19\)	\(16\)	\(3\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(28\)	\(19\)	\(9\)		\(27\)	\(19\)	\(8\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(22\)	\(18\)	\(4\)		\(21\)	\(18\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(25\)	\(16\)	\(9\)		\(24\)	\(16\)	\(8\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(44\)	\(32\)	\(12\)		\(43\)	\(32\)	\(11\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(50\)	\(37\)	\(13\)		\(48\)	\(37\)	\(11\)		\(2\)	\(0\)	\(2\)

Trace form

69 * q - q^2 + 71 * q^4 - 6 * q^5 + 12 * q^6 - q^7 + 3 * q^8 + 69 * q^9 + 6 * q^10 - 4 * q^11 + 12 * q^12 - 10 * q^13 + q^14 - 8 * q^15 + 79 * q^16 - 2 * q^17 - 9 * q^18 + 8 * q^19 - 42 * q^20 + 4 * q^22 + 8 * q^23 + 32 * q^24 + 47 * q^25 + 10 * q^26 - 7 * q^28 - 30 * q^29 + 12 * q^30 + 4 * q^31 - 5 * q^32 - 2 * q^34 - 6 * q^35 + 103 * q^36 - 22 * q^37 - 20 * q^38 - 8 * q^39 + 34 * q^40 - 10 * q^41 + 8 * q^42 + 16 * q^43 + 4 * q^44 - 58 * q^45 - 24 * q^46 - 4 * q^47 - 28 * q^48 + 69 * q^49 - 23 * q^50 + 4 * q^51 - 30 * q^52 - 26 * q^53 + 44 * q^54 - 28 * q^55 - 3 * q^56 + 36 * q^57 + 10 * q^58 + 28 * q^59 - 76 * q^60 - 22 * q^61 - 28 * q^62 - 5 * q^63 + 139 * q^64 - 28 * q^65 - 64 * q^66 - 36 * q^67 - 30 * q^68 - 32 * q^69 + 18 * q^70 - 56 * q^71 - 61 * q^72 - 10 * q^73 - 22 * q^74 - 4 * q^75 - 12 * q^77 - 60 * q^78 - 32 * q^79 - 94 * q^80 + 37 * q^81 - 38 * q^82 - 4 * q^83 - 16 * q^84 - 24 * q^85 - 20 * q^86 - 60 * q^87 + 12 * q^88 - 2 * q^89 - 98 * q^90 - 14 * q^91 - 56 * q^92 - 32 * q^93 + 112 * q^94 - 20 * q^95 + 28 * q^96 + 18 * q^97 - q^98 + 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(973))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	139
973.2.a.a	$973$	$2$	973.a	1.a	$1$	$1$	$1$	$7.769$	\(\Q\)	None	✓	✓			973.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}-2q^{9}-2q^{12}+\cdots\)
973.2.a.b	$973$	$2$	973.a	1.a	$1$	$1$	$1$	$7.769$	\(\Q\)	None	✓	✓			973.2.a.b	$1$	$0$	\(2\)	\(1\)	\(4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
973.2.a.c	$973$	$2$	973.a	1.a	$1$	$2$	$2$	$7.769$	\(\Q(\sqrt{2}) \)	None	✓	✓			973.2.a.c	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{3}+2\beta q^{5}+(2+\beta )q^{6}+\cdots\)
973.2.a.d	$973$	$2$	973.a	1.a	$1$	$3$	$3$	$7.769$	3.3.148.1	None	✓	✓			973.2.a.d	$1$	$0$	\(1\)	\(2\)	\(-2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
973.2.a.e	$973$	$2$	973.a	1.a	$1$	$4$	$4$	$7.769$	4.4.16357.1	None	✓	✓			973.2.a.e	$1$	$0$	\(1\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{3})q^{2}+\beta _{2}q^{3}+(2-\beta _{3})q^{4}+\cdots\)
973.2.a.f	$973$	$2$	973.a	1.a	$1$	$12$	$12$	$7.769$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		973.2.a.f	$1$	$0$	\(4\)	\(6\)	\(11\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
973.2.a.g	$973$	$2$	973.a	1.a	$1$	$15$	$15$	$7.769$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓		973.2.a.g	$1$	$1$	\(-7\)	\(-12\)	\(-19\)	\(15\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{6})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
973.2.a.h	$973$	$2$	973.a	1.a	$1$	$15$	$15$	$7.769$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓		973.2.a.h	$1$	$0$	\(7\)	\(7\)	\(-1\)	\(-15\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
973.2.a.i	$973$	$2$	973.a	1.a	$1$	$16$	$16$	$7.769$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	973.2.a.i	$1$	$1$	\(-9\)	\(-7\)	\(5\)	\(-16\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(973))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(973)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(139))\)\(^{\oplus 2}\)