Space of modular forms of level 4788, weight 2, and Character 4788.dq

• Label: 4788.2.dq
• Level: $4788$
• Weight: $2$
• Character orbit: 4788.dq
• Rep. character: $\chi_{4788}(2357,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $1920$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4788.dq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1920\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4788, [\chi])\).

	Total	New	Old
Modular forms	1968	96	1872
Cusp forms	1872	96	1776
Eisenstein series	96	0	96

Trace form

\( 96 q - 8 q^{7} - 56 q^{25} + 24 q^{31} + 40 q^{43} + 20 q^{49} - 48 q^{67} - 12 q^{73} + 8 q^{79} + 40 q^{85} - 88 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4788, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4788.2.dq.a	$4788$	$2$	4788.dq	21.g	$6$	$96$	$48$	$38.232$		None		✓	✓	✓	4788.2.dq.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4788, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4788, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1596, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2394, [\chi])\)\(^{\oplus 2}\)