Space of modular forms of level 755, weight 1, and Character 755.c

• Label: 755.1.c
• Level: $755$
• Weight: $1$
• Character orbit: 755.c
• Rep. character: $\chi_{755}(754,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $76$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	755.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 755 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(76\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(755, [\chi])\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	11	11	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	11	0	0	0

Trace form

11 * q - 3 * q^4 - 3 * q^9 - 4 * q^11 + 11 * q^16 - 4 * q^19 - 4 * q^21 + 4 * q^25 + 11 * q^36 - 4 * q^39 - 7 * q^40 + 10 * q^44 - 4 * q^45 - 3 * q^49 - 7 * q^50 - 3 * q^64 - 4 * q^69 - 4 * q^76 - 7 * q^80 + 7 * q^81 - 4 * q^84 - 4 * q^91 + 14 * q^94 - 4 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(755, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
755.1.c.a	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-755}) \)	None	✓	✓			755.1.c.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)	$1$		\(q-q^{3}+q^{4}+q^{5}+2q^{7}-q^{11}-q^{12}+\cdots\)
755.1.c.b	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-151}) \), \(\Q(\sqrt{-755}) \)	\(\Q(\sqrt{5}) \)	✓	✓			755.1.c.b	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots\)
755.1.c.c	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-755}) \)	None	✓	✓			755.1.c.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)	$1$		\(q+q^{3}+q^{4}+q^{5}-2q^{7}-q^{11}+q^{12}+\cdots\)
755.1.c.d	$755$	$1$	755.c	755.c	$2$	$2$	$2$	$0.377$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-755}) \)	None	✓	✓			755.1.c.d	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{3}+q^{4}-q^{5}+2q^{9}-q^{11}-\beta q^{12}+\cdots\)
755.1.c.e	$755$	$1$	755.c	755.c	$2$	$6$	$6$	$0.377$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-151}) \)	None		✓	✓		755.1.c.e	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-1-\zeta_{14}^{3}+\cdots)q^{4}+\cdots\)