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

• Label: 3800.1.y
• Level: $3800$
• Weight: $1$
• Character orbit: 3800.y
• Rep. character: $\chi_{3800}(1443,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $7$
• Sturm bound: $600$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3800.y (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(600\)
Trace bound:			\(6\)

Dimensions

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

	Total	New	Old
Modular forms	48	32	16
Cusp forms	24	24	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	24	0	0	0

Trace form

\( 24 q + 8 q^{6} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3800.1.y.a	$3800$	$1$	3800.y	760.y	$4$	$2$	$1$	$1.896$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None		$4$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{2}+(-1-i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\)
3800.1.y.b	$3800$	$1$	3800.y	760.y	$4$	$2$	$1$	$1.896$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+iq^{2}+(-1-i)q^{3}-q^{4}+(1-i+\cdots)q^{6}+\cdots\)
3800.1.y.c	$3800$	$1$	3800.y	760.y	$4$	$2$	$1$	$1.896$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-iq^{2}+(1+i)q^{3}-q^{4}+(1-i)q^{6}+\cdots\)
3800.1.y.d	$3800$	$1$	3800.y	760.y	$4$	$2$	$1$	$1.896$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None		$4$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{2}+(1+i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\)
3800.1.y.e	$3800$	$1$	3800.y	760.y	$4$	$4$	$2$	$1.896$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-95}) \)	\(\Q(\sqrt{190}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-2q^{6}+\cdots\)
3800.1.y.f	$3800$	$1$	3800.y	760.y	$4$	$4$	$2$	$1.896$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-95}) \)	\(\Q(\sqrt{38}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
3800.1.y.g	$3800$	$1$	3800.y	760.y	$4$	$8$	$4$	$1.896$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{3}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{6}q^{4}+\cdots\)