Space of modular forms of level 1824, weight 2, and Character 1824.bg

• Label: 1824.2.bg
• Level: $1824$
• Weight: $2$
• Character orbit: 1824.bg
• Rep. character: $\chi_{1824}(559,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $640$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.bg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(640\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1824, [\chi])\).

	Total	New	Old
Modular forms	672	80	592
Cusp forms	608	80	528
Eisenstein series	64	0	64

Trace form

\( 80 q + 40 q^{9} + 8 q^{19} + 40 q^{25} - 48 q^{35} - 64 q^{49} - 24 q^{51} + 8 q^{57} - 8 q^{73} - 40 q^{81} + 80 q^{83}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1824, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1824.2.bg.a	$1824$	$2$	1824.bg	152.o	$6$	$80$	$40$	$14.565$		None			✓	✓	456.2.y.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1824, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1824, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)