Space of modular forms of level 1872, weight 1, and Character 1872.gc

• Label: 1872.1.gc
• Level: $1872$
• Weight: $1$
• Character orbit: 1872.gc
• Rep. character: $\chi_{1872}(145,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1872.gc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1872, [\chi])\).

	Total	New	Old
Modular forms	112	8	104
Cusp forms	16	4	12
Eisenstein series	96	4	92

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

\( 4 q - 2 q^{7} - 2 q^{19} + 2 q^{31} - 2 q^{37} + 6 q^{43} - 6 q^{49} + 4 q^{67} + 2 q^{73} - 2 q^{91} - 2 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1872, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1872.1.gc.a	$1872$	$1$	1872.gc	13.f	$12$	$4$	$1$	$0.934$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None			✓	✓	468.1.cd.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1872, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)