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

• Label: 3800.1.o
• Level: $3800$
• Weight: $1$
• Character orbit: 3800.o
• Rep. character: $\chi_{3800}(1101,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $7$
• 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.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
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	40	28	12
Cusp forms	28	22	6
Eisenstein series	12	6	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	22	0	0	0

Trace form

22 * q + 14 * q^4 - 2 * q^6 + 2 * q^7 + 20 * q^9 + 14 * q^16 + 2 * q^17 + 2 * q^23 - 10 * q^24 + 6 * q^26 + 2 * q^28 + 4 * q^36 - 2 * q^38 - 10 * q^39 - 2 * q^42 + 8 * q^44 - 4 * q^47 + 4 * q^49 - 2 * q^54 + 2 * q^57 + 2 * q^58 + 14 * q^64 + 8 * q^66 + 2 * q^68 + 2 * q^73 - 8 * q^74 + 18 * q^81 - 2 * q^87 + 2 * q^92 + 6 * q^96

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.o.a	$3800$	$1$	3800.o	152.g	$2$	$1$	$1$	$1.896$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None	✓				152.1.g.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
3800.1.o.b	$3800$	$1$	3800.o	152.g	$2$	$1$	$1$	$1.896$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None	✓				152.1.g.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3800.1.o.c	$3800$	$1$	3800.o	152.g	$2$	$3$	$3$	$1.896$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-38}) \)	None	✓	✓			3800.1.o.c	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.d	$3800$	$1$	3800.o	152.g	$2$	$3$	$3$	$1.896$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-38}) \)	None	✓	✓			3800.1.o.c	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.e	$3800$	$1$	3800.o	152.g	$2$	$3$	$3$	$1.896$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-38}) \)	None	✓	✓			3800.1.o.c	$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.f	$3800$	$1$	3800.o	152.g	$2$	$3$	$3$	$1.896$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-38}) \)	None	✓	✓			3800.1.o.c	$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.g	$3800$	$1$	3800.o	152.g	$2$	$8$	$8$	$1.896$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-95}) \)	None			✓		760.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}q^{2}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)

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

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