Space of modular forms of level 1912, weight 1, and Character 1912.x

• Label: 1912.1.x
• Level: $1912$
• Weight: $1$
• Character orbit: 1912.x
• Rep. character: $\chi_{1912}(501,\cdot)$
• Character field: $\Q(\zeta_{34})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1912 = 2^{3} \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1912.x (of order \(34\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1912 \)
Character field:			\(\Q(\zeta_{34})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1912, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - q^{2} - q^{4} - q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1912, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1912.1.x.a	$1912$	$1$	1912.x	1912.x	$34$	$16$	$1$	$0.954$	\(\Q(\zeta_{34})\)	$D_{34}$	None	\(\Q(\sqrt{2}) \)		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{34}^{6}q^{2}+\zeta_{34}^{12}q^{4}+(\zeta_{34}^{4}+\zeta_{34}^{7}+\cdots)q^{7}+\cdots\)