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

• Label: 3800.1.bd
• Level: $3800$
• Weight: $1$
• Character orbit: 3800.bd
• Rep. character: $\chi_{3800}(1451,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $14$
• Newform subspaces: $6$
• Sturm bound: $600$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3800.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(600\)
Trace bound:			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	44	26	18
Cusp forms	20	14	6
Eisenstein series	24	12	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	14	0	0	0

Trace form

14 * q + q^2 - q^3 - 3 * q^4 - q^6 - 2 * q^8 - 4 * q^9 - 2 * q^11 + 2 * q^12 - 2 * q^14 - 7 * q^16 + 2 * q^17 + 3 * q^19 - q^22 - q^24 + 8 * q^26 - 2 * q^27 + q^32 + q^33 + 2 * q^34 - 8 * q^36 - 2 * q^38 + q^41 + 2 * q^43 - 3 * q^44 - 4 * q^46 - q^48 + 10 * q^49 + 4 * q^51 - 11 * q^54 - 4 * q^56 + 2 * q^57 + 9 * q^59 + 6 * q^64 + 7 * q^66 - q^67 - 4 * q^68 - q^73 - 2 * q^74 + 5 * q^76 - 9 * q^81 - q^82 + 2 * q^83 - 10 * q^86 + 2 * q^88 + 4 * q^91 - 8 * q^94 + 2 * q^96 - q^97 + q^98 + 4 * q^99

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.bd.a	$3800$	$1$	3800.bd	152.k	$6$	$2$	$1$	$1.896$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.bd.a	$4$	$0$	\(-1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots\)
3800.1.bd.b	$3800$	$1$	3800.bd	152.k	$6$	$2$	$1$	$1.896$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.bd.b	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.c	$3800$	$1$	3800.bd	152.k	$6$	$2$	$1$	$1.896$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None					152.1.k.a	$4$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.d	$3800$	$1$	3800.bd	152.k	$6$	$2$	$1$	$1.896$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.bd.b	$4$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.e	$3800$	$1$	3800.bd	152.k	$6$	$2$	$1$	$1.896$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		✓			3800.1.bd.a	$4$	$0$	\(1\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots\)
3800.1.bd.f	$3800$	$1$	3800.bd	152.k	$6$	$4$	$2$	$1.896$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None			✓		760.1.bm.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{7}+\cdots\)

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

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