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

• Label: 3800.1.cv
• Level: $3800$
• Weight: $1$
• Character orbit: 3800.cv
• Rep. character: $\chi_{3800}(251,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $42$
• Newform subspaces: $6$
• Sturm bound: $600$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3800.cv (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(600\)
Trace bound:			\(22\)

Dimensions

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

	Total	New	Old
Modular forms	132	78	54
Cusp forms	60	42	18
Eisenstein series	72	36	36

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	42	0	0	0

Trace form

\( 42 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} + O(q^{10}) \)

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	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.cv.a	$3800$	$1$	3800.cv	152.u	$18$	$6$	$1$	$1.896$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.cv.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.b	$3800$	$1$	3800.cv	152.u	$18$	$6$	$1$	$1.896$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.cv.b	$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.c	$3800$	$1$	3800.cv	152.u	$18$	$6$	$1$	$1.896$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None					152.1.u.a	$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots\)
3800.1.cv.d	$3800$	$1$	3800.cv	152.u	$18$	$6$	$1$	$1.896$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.cv.b	$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+(\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.e	$3800$	$1$	3800.cv	152.u	$18$	$6$	$1$	$1.896$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.cv.a	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.f	$3800$	$1$	3800.cv	152.u	$18$	$12$	$2$	$1.896$	\(\Q(\zeta_{36})\)	$D_{9}$	\(\Q(\sqrt{-10}) \)	None			✓		760.1.bz.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}^{13}-\zeta_{36}^{17}+\cdots)q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3800, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)