Space of modular forms of level 1083, weight 2, and trivial character

• Label: 1083.2.a
• Level: $1083$
• Weight: $2$
• Character orbit: 1083.a
• Rep. character: $\chi_{1083}(1,\cdot)$
• Character field: $\Q$
• Dimension: $57$
• Newform subspaces: $19$
• Sturm bound: $253$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1083.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(253\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1083))\).

	Total	New	Old
Modular forms	146	57	89
Cusp forms	107	57	50
Eisenstein series	39	0	39

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

\(3\)	\(19\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(33\)	\(14\)	\(19\)		\(24\)	\(14\)	\(10\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)		\(39\)	\(15\)	\(24\)		\(29\)	\(15\)	\(14\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(-\)		\(40\)	\(19\)	\(21\)		\(30\)	\(19\)	\(11\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(+\)		\(34\)	\(9\)	\(25\)		\(24\)	\(9\)	\(15\)		\(10\)	\(0\)	\(10\)
Plus space		\(+\)		\(67\)	\(23\)	\(44\)		\(48\)	\(23\)	\(25\)		\(19\)	\(0\)	\(19\)
Minus space		\(-\)		\(79\)	\(34\)	\(45\)		\(59\)	\(34\)	\(25\)		\(20\)	\(0\)	\(20\)

Trace form

57 * q + 3 * q^2 - q^3 + 57 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 57 * q^9 - 2 * q^10 + q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + 69 * q^16 + 2 * q^17 + 3 * q^18 - 6 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 3 * q^24 + 59 * q^25 - 14 * q^26 - q^27 - 4 * q^28 + 10 * q^29 + 10 * q^30 - 4 * q^31 - 21 * q^32 + 4 * q^33 + 10 * q^34 - 28 * q^35 + 57 * q^36 + 2 * q^37 + 2 * q^39 - 6 * q^40 + 10 * q^41 + 16 * q^42 + 4 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 - 8 * q^47 + q^48 + 45 * q^49 + q^50 + 2 * q^51 + 14 * q^52 + 2 * q^53 - q^54 - 4 * q^55 - 30 * q^58 + 20 * q^59 - 10 * q^60 - 10 * q^61 - 28 * q^62 + 57 * q^64 + 24 * q^65 - 12 * q^66 - 12 * q^67 - 30 * q^68 - 12 * q^69 + 36 * q^70 + 3 * q^72 + 6 * q^73 + 14 * q^74 + 9 * q^75 - 8 * q^77 - 22 * q^78 - 16 * q^79 - 30 * q^80 + 57 * q^81 - 30 * q^82 - 40 * q^83 - 16 * q^84 - 40 * q^85 + 6 * q^87 - 2 * q^89 - 2 * q^90 + 28 * q^91 - 28 * q^92 - 20 * q^93 - 24 * q^94 - 5 * q^96 + 2 * q^97 + 47 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	19
1083.2.a.a	$1083$	$2$	1083.a	1.a	$1$	$1$	$1$	$8.648$	\(\Q\)	None	✓				57.2.a.c	$1$	$0$	\(-1\)	\(-1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
1083.2.a.b	$1083$	$2$	1083.a	1.a	$1$	$1$	$1$	$8.648$	\(\Q\)	None	✓				57.2.e.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
1083.2.a.c	$1083$	$2$	1083.a	1.a	$1$	$1$	$1$	$8.648$	\(\Q\)	None	✓				57.2.e.a	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
1083.2.a.d	$1083$	$2$	1083.a	1.a	$1$	$1$	$1$	$8.648$	\(\Q\)	None	✓				57.2.a.b	$1$	$0$	\(2\)	\(-1\)	\(1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
1083.2.a.e	$1083$	$2$	1083.a	1.a	$1$	$1$	$1$	$8.648$	\(\Q\)	None	✓				57.2.a.a	$1$	$1$	\(2\)	\(1\)	\(-3\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
1083.2.a.f	$1083$	$2$	1083.a	1.a	$1$	$2$	$2$	$8.648$	\(\Q(\sqrt{5}) \)	None	✓	✓			1083.2.a.f	$1$	$1$	\(-3\)	\(2\)	\(1\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
1083.2.a.g	$1083$	$2$	1083.a	1.a	$1$	$2$	$2$	$8.648$	\(\Q(\sqrt{17}) \)	None	✓	✓			1083.2.a.g	$1$	$1$	\(-1\)	\(-2\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1083.2.a.h	$1083$	$2$	1083.a	1.a	$1$	$2$	$2$	$8.648$	\(\Q(\sqrt{5}) \)	None	✓	✓			1083.2.a.h	$1$	$1$	\(-1\)	\(2\)	\(-1\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(1-3\beta )q^{5}+\cdots\)
1083.2.a.i	$1083$	$2$	1083.a	1.a	$1$	$2$	$2$	$8.648$	\(\Q(\sqrt{5}) \)	None	✓	✓			1083.2.a.h	$1$	$0$	\(1\)	\(-2\)	\(-1\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-3\beta )q^{5}+\cdots\)
1083.2.a.j	$1083$	$2$	1083.a	1.a	$1$	$2$	$2$	$8.648$	\(\Q(\sqrt{17}) \)	None	✓	✓			1083.2.a.g	$1$	$0$	\(1\)	\(2\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1083.2.a.k	$1083$	$2$	1083.a	1.a	$1$	$2$	$2$	$8.648$	\(\Q(\sqrt{5}) \)	None	✓	✓			1083.2.a.f	$1$	$0$	\(3\)	\(-2\)	\(1\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1083.2.a.l	$1083$	$2$	1083.a	1.a	$1$	$3$	$3$	$8.648$	3.3.564.1	None	✓				57.2.e.b	$1$	$0$	\(-1\)	\(3\)	\(2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1083.2.a.m	$1083$	$2$	1083.a	1.a	$1$	$3$	$3$	$8.648$	\(\Q(\zeta_{18})^+\)	None	✓				57.2.i.a	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1083.2.a.n	$1083$	$2$	1083.a	1.a	$1$	$3$	$3$	$8.648$	\(\Q(\zeta_{18})^+\)	None	✓		✓		57.2.i.a	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1083.2.a.o	$1083$	$2$	1083.a	1.a	$1$	$3$	$3$	$8.648$	3.3.564.1	None	✓				57.2.e.b	$1$	$0$	\(1\)	\(-3\)	\(2\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1083.2.a.p	$1083$	$2$	1083.a	1.a	$1$	$6$	$6$	$8.648$	6.6.6357609.1	None	✓		✓		57.2.i.b	$1$	$0$	\(0\)	\(-6\)	\(9\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1083.2.a.q	$1083$	$2$	1083.a	1.a	$1$	$6$	$6$	$8.648$	6.6.6357609.1	None	✓				57.2.i.b	$1$	$0$	\(0\)	\(6\)	\(9\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1083.2.a.r	$1083$	$2$	1083.a	1.a	$1$	$8$	$8$	$8.648$	8.8.9764000000.1	None	✓	✓	✓		1083.2.a.r	$1$	$1$	\(-4\)	\(-8\)	\(-2\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1083.2.a.s	$1083$	$2$	1083.a	1.a	$1$	$8$	$8$	$8.648$	8.8.9764000000.1	None	✓	✓	✓		1083.2.a.r	$1$	$0$	\(4\)	\(8\)	\(-2\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1083))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1083)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)