Space of modular forms of level 2064, weight 2, and Character 2064.d

• Label: 2064.2.d
• Level: $2064$
• Weight: $2$
• Character orbit: 2064.d
• Rep. character: $\chi_{2064}(431,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $3$
• Sturm bound: $704$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2064 = 2^{4} \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2064.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(704\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2064, [\chi])\).

	Total	New	Old
Modular forms	364	84	280
Cusp forms	340	84	256
Eisenstein series	24	0	24

Trace form

\( 84 q - 108 q^{25} + 48 q^{37} - 24 q^{45} - 60 q^{49} + 48 q^{57} - 48 q^{61} - 24 q^{69} + 24 q^{73} - 48 q^{81} + 72 q^{93} - 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2064, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2064.2.d.a	$2064$	$2$	2064.d	12.b	$2$	$8$	$8$	$16.481$	\(\Q(\zeta_{24})\)	None		✓			2064.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{6}+\beta_{5}+\beta_1)q^{3}+\beta_{7} q^{5}+(-2\beta_{2}-\beta_1)q^{7}+\cdots\)
2064.2.d.b	$2064$	$2$	2064.d	12.b	$2$	$28$	$28$	$16.481$		None		✓			2064.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2064.2.d.c	$2064$	$2$	2064.d	12.b	$2$	$48$	$48$	$16.481$		None		✓	✓		2064.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2064, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(516, [\chi])\)\(^{\oplus 3}\)