Space of modular forms of level 1824, weight 1, and Character 1824.ba

• Label: 1824.1.ba
• Level: $1824$
• Weight: $1$
• Character orbit: 1824.ba
• Rep. character: $\chi_{1824}(335,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $320$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1824.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(320\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1824, [\chi])\).

	Total	New	Old
Modular forms	48	12	36
Cusp forms	16	4	12
Eisenstein series	32	8	24

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 3 q^{3} + q^{9} - 2 q^{19} + 2 q^{25} - 3 q^{33} - 4 q^{43} + 4 q^{49} + 6 q^{67} - 2 q^{73} + q^{81} - 6 q^{97} - 3 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1824, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1824.1.ba.a	$1824$	$1$	1824.ba	456.s	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None					456.1.s.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{11}+\cdots\)
1824.1.ba.b	$1824$	$1$	1824.ba	456.s	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None					456.1.s.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1824, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1824, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 3}\)