Space of modular forms of level 3775, weight 1, and Character 3775.d

• Label: 3775.1.d
• Level: $3775$
• Weight: $1$
• Character orbit: 3775.d
• Rep. character: $\chi_{3775}(301,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $7$
• Sturm bound: $380$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 3775 = 5^{2} \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3775.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 151 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(380\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3775, [\chi])\).

	Total	New	Old
Modular forms	37	25	12
Cusp forms	31	22	9
Eisenstein series	6	3	3

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	8

Trace form

22 * q + q^2 + 9 * q^4 + 2 * q^8 + 6 * q^9 - 5 * q^11 + 12 * q^16 + q^17 + q^18 + 11 * q^19 - 8 * q^21 + 2 * q^22 - q^29 + 3 * q^31 + 3 * q^32 - 6 * q^34 + 13 * q^36 + q^37 - 5 * q^38 + q^43 - 6 * q^44 + q^47 + 2 * q^49 - 5 * q^58 + 7 * q^59 + 2 * q^62 - q^64 - 4 * q^68 + 12 * q^69 + 2 * q^72 - 10 * q^74 - 3 * q^76 + 2 * q^81 - 8 * q^84 - 6 * q^86 + 4 * q^88 + 4 * q^91 - 17 * q^94 + q^97 + q^98 + 3 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(3775, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3775.1.d.a	$3775$	$1$	3775.d	151.b	$2$	$1$	$1$	$1.884$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-151}) \), \(\Q(\sqrt{-755}) \)	\(\Q(\sqrt{5}) \)	✓				755.1.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{4}+q^{9}+2q^{11}+q^{16}-2q^{19}+\cdots\)
3775.1.d.b	$3775$	$1$	3775.d	151.b	$2$	$2$	$2$	$1.884$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-755}) \)	None					755.1.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots\)
3775.1.d.c	$3775$	$1$	3775.d	151.b	$2$	$2$	$2$	$1.884$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-755}) \)	None					755.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{3}-q^{4}-2 i q^{7}-q^{11}+i q^{12}+\cdots\)
3775.1.d.d	$3775$	$1$	3775.d	151.b	$2$	$3$	$3$	$1.884$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-151}) \)	None	✓				151.1.b.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{8}+\cdots\)
3775.1.d.e	$3775$	$1$	3775.d	151.b	$2$	$4$	$4$	$1.884$	\(\Q(i, \sqrt{5})\)	$A_{5}$	None	None		✓			3775.1.d.e	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{1}q^{6}+\cdots\)
3775.1.d.f	$3775$	$1$	3775.d	151.b	$2$	$4$	$4$	$1.884$	\(\Q(i, \sqrt{5})\)	$A_{5}$	None	None		✓			3775.1.d.e	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-\beta _{1}q^{6}+\cdots\)
3775.1.d.g	$3775$	$1$	3775.d	151.b	$2$	$6$	$6$	$1.884$	\(\Q(\zeta_{28})^+\)	$D_{14}$	\(\Q(\sqrt{-151}) \)	None	✓		✓		755.1.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3775, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3775, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(151, [\chi])\)\(^{\oplus 3}\)