Space of modular forms of level 913, weight 2, and trivial character

• Label: 913.2.a
• Level: $913$
• Weight: $2$
• Character orbit: 913.a
• Rep. character: $\chi_{913}(1,\cdot)$
• Character field: $\Q$
• Dimension: $67$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 913 = 11 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	913.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(913))\).

	Total	New	Old
Modular forms	86	67	19
Cusp forms	83	67	16
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.

\(11\)	\(83\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(17\)	\(16\)	\(1\)		\(17\)	\(16\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(26\)	\(19\)	\(7\)		\(25\)	\(19\)	\(6\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(20\)	\(17\)	\(3\)		\(19\)	\(17\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(23\)	\(15\)	\(8\)		\(22\)	\(15\)	\(7\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(40\)	\(31\)	\(9\)		\(39\)	\(31\)	\(8\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(46\)	\(36\)	\(10\)		\(44\)	\(36\)	\(8\)		\(2\)	\(0\)	\(2\)

Trace form

67 * q + q^2 - 2 * q^3 + 67 * q^4 - 4 * q^5 - 4 * q^7 - 15 * q^8 + 69 * q^9 - 6 * q^10 - 3 * q^11 - 4 * q^12 - 22 * q^13 + 12 * q^14 + 2 * q^15 + 79 * q^16 - 10 * q^17 + 17 * q^18 + 2 * q^20 - 4 * q^21 + 3 * q^22 + 10 * q^23 + 36 * q^24 + 55 * q^25 + 6 * q^26 - 50 * q^27 - 28 * q^28 + 14 * q^29 - 24 * q^30 - 18 * q^31 - 39 * q^32 - 2 * q^33 - 6 * q^34 - 12 * q^35 + 63 * q^36 - 40 * q^37 + 28 * q^38 - 16 * q^39 - 2 * q^40 + 10 * q^41 + 12 * q^43 - 3 * q^44 - 2 * q^45 + 64 * q^46 - 12 * q^47 - 44 * q^48 + 51 * q^49 - 77 * q^50 + 32 * q^51 - 74 * q^52 - 18 * q^53 + 8 * q^54 + 60 * q^56 + 12 * q^57 - 38 * q^58 - 2 * q^59 - 24 * q^60 - 26 * q^61 - 8 * q^62 - 28 * q^63 + 55 * q^64 + 12 * q^65 + 12 * q^66 + 2 * q^67 - 34 * q^68 + 42 * q^69 - 48 * q^70 + 10 * q^71 - 51 * q^72 - 54 * q^73 - 34 * q^74 + 4 * q^75 + 8 * q^76 - 4 * q^77 - 32 * q^78 - 12 * q^79 + 30 * q^80 + 107 * q^81 - 74 * q^82 + q^83 - 56 * q^84 - 36 * q^85 - 60 * q^86 - 20 * q^87 - 9 * q^88 + 12 * q^89 - 58 * q^90 - 16 * q^91 - 6 * q^93 + 44 * q^94 - 24 * q^95 + 52 * q^96 - 40 * q^97 + 73 * q^98 - 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(913))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	83
913.2.a.a	$913$	$2$	913.a	1.a	$1$	$1$	$1$	$7.290$	\(\Q\)	None	✓	✓			913.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{7}+3q^{8}-3q^{9}-q^{11}+\cdots\)
913.2.a.b	$913$	$2$	913.a	1.a	$1$	$1$	$1$	$7.290$	\(\Q\)	None	✓	✓			913.2.a.b	$1$	$0$	\(2\)	\(3\)	\(3\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+2q^{4}+3q^{5}+6q^{6}+\cdots\)
913.2.a.c	$913$	$2$	913.a	1.a	$1$	$5$	$5$	$7.290$	5.5.176281.1	None	✓	✓			913.2.a.c	$1$	$0$	\(1\)	\(1\)	\(3\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{2}-2\beta _{4})q^{5}+\cdots\)
913.2.a.d	$913$	$2$	913.a	1.a	$1$	$12$	$12$	$7.290$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		913.2.a.d	$1$	$0$	\(2\)	\(4\)	\(-1\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
913.2.a.e	$913$	$2$	913.a	1.a	$1$	$15$	$15$	$7.290$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	913.2.a.e	$1$	$1$	\(-7\)	\(-7\)	\(-4\)	\(-17\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
913.2.a.f	$913$	$2$	913.a	1.a	$1$	$16$	$16$	$7.290$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	913.2.a.f	$1$	$1$	\(-5\)	\(-8\)	\(-7\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
913.2.a.g	$913$	$2$	913.a	1.a	$1$	$17$	$17$	$7.290$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	913.2.a.g	$1$	$0$	\(9\)	\(5\)	\(2\)	\(13\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{8}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(913))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(913)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(83))\)\(^{\oplus 2}\)