Space of modular forms of level 2034, weight 3, and Character 2034.d

• Label: 2034.3.d
• Level: $2034$
• Weight: $3$
• Character orbit: 2034.d
• Rep. character: $\chi_{2034}(2033,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $2$
• Sturm bound: $1026$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2034 = 2 \cdot 3^{2} \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2034.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 339 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1026\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2034, [\chi])\).

	Total	New	Old
Modular forms	692	76	616
Cusp forms	676	76	600
Eisenstein series	16	0	16

Trace form

\( 76 q - 152 q^{4} - 32 q^{13} + 304 q^{16} + 236 q^{25} - 32 q^{31} + 564 q^{49} + 64 q^{52} + 40 q^{61} - 608 q^{64} + 168 q^{82} - 224 q^{85} + 536 q^{91} - 456 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2034, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2034.3.d.a	$2034$	$3$	2034.d	339.c	$2$	$36$	$36$	$55.422$		None		✓			2034.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$
2034.3.d.b	$2034$	$3$	2034.d	339.c	$2$	$40$	$40$	$55.422$		None		✓	✓		2034.3.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2034, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2034, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(339, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(678, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1017, [\chi])\)\(^{\oplus 2}\)