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

• Label: 1900.1.w
• Level: $1900$
• Weight: $1$
• Character orbit: 1900.w
• Rep. character: $\chi_{1900}(189,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $300$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1900.w (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 475 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(300\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	44	8	36
Cusp forms	20	8	12
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + q^{5} + 2 q^{9} + 3 q^{11} - 5 q^{17} - 2 q^{19} - 10 q^{23} + q^{25} - 2 q^{35} - q^{45} - 6 q^{49} + q^{55} - 2 q^{61} + 5 q^{63} - 2 q^{81} + 10 q^{83} + 2 q^{85} + q^{95} + 2 q^{99}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.1.w.a	$1900$	$1$	1900.w	475.m	$10$	$8$	$2$	$0.948$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-19}) \)	None		✓	✓	✓	1900.1.w.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{30}^{8}q^{5}+(\zeta_{30}^{2}+\zeta_{30}^{13})q^{7}+\zeta_{30}^{3}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)