Space of modular forms of level 1900, weight 1, and Character 1900.j

• Label: 1900.1.j
• Level: $1900$
• Weight: $1$
• Character orbit: 1900.j
• Rep. character: $\chi_{1900}(607,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $300$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1900.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(300\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1900, [\chi])\).

	Total	New	Old
Modular forms	40	24	16
Cusp forms	16	16	0
Eisenstein series	24	8	16

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

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1900, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.1.j.a	$1900$	$1$	1900.j	380.j	$4$	$8$	$4$	$0.948$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-95}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\)
1900.1.j.b	$1900$	$1$	1900.j	380.j	$4$	$8$	$4$	$0.948$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-95}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{3}q^{2}+(\zeta_{16}+\zeta_{16}^{3})q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)