Space of modular forms of level 5243, weight 2, and trivial character

• Label: 5243.2.a
• Level: $5243$
• Weight: $2$
• Character orbit: 5243.a
• Rep. character: $\chi_{5243}(1,\cdot)$
• Character field: $\Q$
• Dimension: $362$
• Newform subspaces: $18$
• Sturm bound: $1008$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 5243 = 7^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5243.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1008\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5243))\).

	Total	New	Old
Modular forms	512	362	150
Cusp forms	497	362	135
Eisenstein series	15	0	15

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

\(7\)	\(107\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(116\)	\(77\)	\(39\)		\(113\)	\(77\)	\(36\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)		\(140\)	\(101\)	\(39\)		\(136\)	\(101\)	\(35\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)		\(140\)	\(101\)	\(39\)		\(136\)	\(101\)	\(35\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)		\(116\)	\(83\)	\(33\)		\(112\)	\(83\)	\(29\)		\(4\)	\(0\)	\(4\)
Plus space		\(+\)		\(232\)	\(160\)	\(72\)		\(225\)	\(160\)	\(65\)		\(7\)	\(0\)	\(7\)
Minus space		\(-\)		\(280\)	\(202\)	\(78\)		\(272\)	\(202\)	\(70\)		\(8\)	\(0\)	\(8\)

Trace form

362 * q + q^2 + 361 * q^4 + 4 * q^5 + 6 * q^6 + 9 * q^8 + 360 * q^9 + 12 * q^10 - 6 * q^11 + 6 * q^12 - 4 * q^13 - 2 * q^15 + 367 * q^16 + 2 * q^17 - 7 * q^18 - 18 * q^19 + 20 * q^20 + 2 * q^22 - 14 * q^23 - 10 * q^24 + 376 * q^25 + 18 * q^26 + 15 * q^27 + 9 * q^29 - 20 * q^30 + 2 * q^31 - q^32 + 11 * q^33 - 22 * q^34 + 317 * q^36 + 34 * q^37 - 2 * q^38 + 27 * q^39 + 24 * q^40 + 8 * q^43 - 12 * q^44 + 42 * q^45 - 4 * q^46 + q^47 - 7 * q^50 - 42 * q^51 - 20 * q^52 + 56 * q^53 + 4 * q^54 + 12 * q^55 - 23 * q^57 + 48 * q^58 - 50 * q^60 - 6 * q^61 + 18 * q^62 + 365 * q^64 + 2 * q^65 - 8 * q^66 + 14 * q^67 + 4 * q^68 + 17 * q^69 - 26 * q^71 + 37 * q^72 - 16 * q^73 + 12 * q^74 - 8 * q^75 - 34 * q^76 - 4 * q^78 + 12 * q^79 + 82 * q^80 + 330 * q^81 + 76 * q^82 - 37 * q^83 + 20 * q^85 + 2 * q^86 - 38 * q^87 + 46 * q^88 + 24 * q^89 + 18 * q^90 - 44 * q^92 + 30 * q^93 + 20 * q^94 + 20 * q^95 - 86 * q^96 - 10 * q^97 - 71 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5243))\) 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	107
5243.2.a.a	$5243$	$2$	5243.a	1.a	$1$	$1$	$1$	$41.866$	\(\Q\)	None	✓				749.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+3q^{8}+\cdots\)
5243.2.a.b	$5243$	$2$	5243.a	1.a	$1$	$2$	$2$	$41.866$	\(\Q(\sqrt{5}) \)	None	✓				107.2.a.a	$1$	$0$	\(-1\)	\(3\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(2+\cdots)q^{5}+\cdots\)
5243.2.a.c	$5243$	$2$	5243.a	1.a	$1$	$4$	$4$	$41.866$	\(\Q(\zeta_{24})^+\)	None	✓	✓			5243.2.a.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{3})q^{5}+\cdots\)
5243.2.a.d	$5243$	$2$	5243.a	1.a	$1$	$4$	$4$	$41.866$	4.4.9248.1	None	✓	✓			5243.2.a.d	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
5243.2.a.e	$5243$	$2$	5243.a	1.a	$1$	$6$	$6$	$41.866$	6.6.113100800.2	None	✓	✓			5243.2.a.e	$2$	$1$	\(-6\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
5243.2.a.f	$5243$	$2$	5243.a	1.a	$1$	$6$	$6$	$41.866$	6.6.2661761.1	None	✓				749.2.a.b	$1$	$1$	\(-1\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
5243.2.a.g	$5243$	$2$	5243.a	1.a	$1$	$7$	$7$	$41.866$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				107.2.a.b	$1$	$1$	\(-1\)	\(-3\)	\(-5\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\beta _{5})q^{4}+\cdots\)
5243.2.a.h	$5243$	$2$	5243.a	1.a	$1$	$10$	$10$	$41.866$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			5243.2.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}-\beta _{8}q^{3}+(2-\beta _{7})q^{4}+(\beta _{8}+\cdots)q^{5}+\cdots\)
5243.2.a.i	$5243$	$2$	5243.a	1.a	$1$	$12$	$12$	$41.866$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				749.2.a.c	$1$	$0$	\(0\)	\(5\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5243.2.a.j	$5243$	$2$	5243.a	1.a	$1$	$14$	$14$	$41.866$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				749.2.a.d	$1$	$1$	\(1\)	\(-5\)	\(-2\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
5243.2.a.k	$5243$	$2$	5243.a	1.a	$1$	$20$	$20$	$41.866$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓				749.2.a.e	$1$	$0$	\(2\)	\(-3\)	\(2\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
5243.2.a.l	$5243$	$2$	5243.a	1.a	$1$	$32$	$32$	$41.866$		None	✓	✓			5243.2.a.l	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5243.2.a.m	$5243$	$2$	5243.a	1.a	$1$	$35$	$35$	$41.866$		None	✓		✓		749.2.e.a	$1$	$1$	\(0\)	\(-11\)	\(-13\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
5243.2.a.n	$5243$	$2$	5243.a	1.a	$1$	$35$	$35$	$41.866$		None	✓				749.2.e.b	$1$	$1$	\(0\)	\(-9\)	\(-15\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5243.2.a.o	$5243$	$2$	5243.a	1.a	$1$	$35$	$35$	$41.866$		None	✓		✓		749.2.e.b	$1$	$0$	\(0\)	\(9\)	\(15\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5243.2.a.p	$5243$	$2$	5243.a	1.a	$1$	$35$	$35$	$41.866$		None	✓				749.2.e.a	$1$	$0$	\(0\)	\(11\)	\(13\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
5243.2.a.q	$5243$	$2$	5243.a	1.a	$1$	$38$	$38$	$41.866$		None	✓	✓	✓		5243.2.a.q	$2$	$1$	\(-6\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5243.2.a.r	$5243$	$2$	5243.a	1.a	$1$	$66$	$66$	$41.866$		None	✓	✓	✓		5243.2.a.r	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5243))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5243)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(107))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(749))\)\(^{\oplus 2}\)