Space of modular forms of level 1083, weight 2, and Character 1083.d

• Label: 1083.2.d
• Level: $1083$
• Weight: $2$
• Character orbit: 1083.d
• Rep. character: $\chi_{1083}(1082,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $5$
• Sturm bound: $253$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1083.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(253\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1083, [\chi])\).

	Total	New	Old
Modular forms	146	130	16
Cusp forms	106	98	8
Eisenstein series	40	32	8

Trace form

98 * q + 84 * q^4 + 4 * q^6 - 4 * q^7 + 8 * q^9 + 64 * q^16 - 16 * q^24 - 30 * q^25 - 12 * q^30 - 8 * q^36 - 44 * q^39 - 38 * q^42 + 28 * q^43 + 20 * q^45 + 10 * q^49 - 26 * q^54 - 12 * q^55 + 8 * q^61 + 14 * q^63 - 56 * q^64 + 82 * q^66 + 8 * q^73 - 60 * q^82 - 68 * q^85 - 18 * q^87 + 16 * q^93 - 26 * q^96 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1083, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1083.2.d.a	$1083$	$2$	1083.d	57.d	$2$	$6$	$6$	$8.648$	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)					57.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 19^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_1 q^{3}-2 q^{4}-\beta_{3} q^{7}-3 q^{9}+\cdots\)
1083.2.d.b	$1083$	$2$	1083.d	57.d	$2$	$8$	$8$	$8.648$	\(\Q(\zeta_{24})\)	None					57.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{2}+(\beta_{6}+\beta_{5}-\beta_1)q^{3}+\beta_{3} q^{4}+\cdots\)
1083.2.d.c	$1083$	$2$	1083.d	57.d	$2$	$12$	$12$	$8.648$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1083.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+\beta _{1}q^{3}+(1-\beta _{3}-\beta _{9})q^{4}+\cdots\)
1083.2.d.d	$1083$	$2$	1083.d	57.d	$2$	$24$	$24$	$8.648$		None					57.2.j.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{2}]$
1083.2.d.e	$1083$	$2$	1083.d	57.d	$2$	$48$	$48$	$8.648$		None		✓	✓		1083.2.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1083, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1083, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)