Space of modular forms of level 768, weight 1, and Character 768.e

• Label: 768.1.e
• Level: $768$
• Weight: $1$
• Character orbit: 768.e
• Rep. character: $\chi_{768}(257,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	768.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(768, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	4	4	0
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(768, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
768.1.e.a	$768$	$1$	768.e	3.b	$2$	$1$	$1$	$0.383$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{6}) \)	✓				192.1.h.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{3}+q^{9}+2q^{19}+q^{25}-q^{27}+\cdots\)
768.1.e.b	$768$	$1$	768.e	3.b	$2$	$1$	$1$	$0.383$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{6}) \)	✓				192.1.h.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{9}-2q^{19}+q^{25}+q^{27}+\cdots\)
768.1.e.c	$768$	$1$	768.e	3.b	$2$	$2$	$2$	$0.383$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{3}) \)			✓		384.1.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{3}-q^{9}-2 i q^{11}+q^{25}+i q^{27}+\cdots\)