Space of modular forms of level 3800, weight 1, and Character 3800.b

• Label: 3800.1.b
• Level: $3800$
• Weight: $1$
• Character orbit: 3800.b
• Rep. character: $\chi_{3800}(949,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $600$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3800.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(600\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3800, [\chi])\).

	Total	New	Old
Modular forms	44	20	24
Cusp forms	32	16	16
Eisenstein series	12	4	8

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

\( 16 q - 16 q^{4} - 4 q^{6} - 12 q^{9} + 16 q^{16} + 4 q^{24} - 4 q^{26} + 12 q^{36} + 8 q^{39} - 12 q^{49} + 8 q^{54} - 16 q^{64} + 4 q^{74} + 8 q^{81} - 4 q^{96}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3800, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3800.1.b.a	$3800$	$1$	3800.b	760.b	$2$	$2$	$2$	$1.896$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None					152.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{2}-i q^{3}-q^{4}-q^{6}-i q^{7}+\cdots\)
3800.1.b.b	$3800$	$1$	3800.b	760.b	$2$	$2$	$2$	$1.896$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None					152.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
3800.1.b.c	$3800$	$1$	3800.b	760.b	$2$	$6$	$6$	$1.896$	6.0.419904.1	$D_{9}$	\(\Q(\sqrt{-38}) \)	None		✓			3800.1.o.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{4}q^{6}+\beta _{1}q^{7}+\cdots\)
3800.1.b.d	$3800$	$1$	3800.b	760.b	$2$	$6$	$6$	$1.896$	6.0.419904.1	$D_{9}$	\(\Q(\sqrt{-38}) \)	None		✓			3800.1.o.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{5})q^{3}-q^{4}-\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3800, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)