Space of modular forms of level 1264, weight 1, and Character 1264.e

• Label: 1264.1.e
• Level: $1264$
• Weight: $1$
• Character orbit: 1264.e
• Rep. character: $\chi_{1264}(1105,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $160$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1264.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(160\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1264, [\chi])\).

	Total	New	Old
Modular forms	18	3	15
Cusp forms	12	2	10
Eisenstein series	6	1	5

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

2 * q - q^5 + 2 * q^9 + q^11 - q^13 + q^19 + q^23 + q^25 + q^31 - q^45 + 2 * q^49 + 2 * q^55 - 2 * q^65 + q^67 - q^73 - 2 * q^79 + 2 * q^81 - 4 * q^83 - q^89 - 3 * q^95 - q^97 + q^99

Decomposition of \(S_{1}^{\mathrm{new}}(1264, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1264.1.e.a	$1264$	$1$	1264.e	79.b	$2$	$2$	$2$	$0.631$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-79}) \)	None	✓		✓	✓	79.1.b.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\beta q^{5}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1264, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1264, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 5}\)