Space of modular forms of level 795, weight 1, and Character 795.x

• Label: 795.1.x
• Level: $795$
• Weight: $1$
• Character orbit: 795.x
• Rep. character: $\chi_{795}(44,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 795 = 3 \cdot 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	795.x (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 795 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(795, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	24	24	0
Eisenstein series	48	48	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

24 * q - 6 * q^4 - 4 * q^6 - 2 * q^9 + 22 * q^10 - 2 * q^15 - 10 * q^16 - 4 * q^19 - 8 * q^24 - 2 * q^25 - 4 * q^31 - 8 * q^34 - 6 * q^36 - 8 * q^40 - 8 * q^46 - 2 * q^49 - 4 * q^51 - 4 * q^54 - 6 * q^60 + 22 * q^61 - 14 * q^64 - 4 * q^69 - 12 * q^76 - 4 * q^79 - 2 * q^81 - 4 * q^85 + 22 * q^90 + 18 * q^94 + 14 * q^96

Decomposition of \(S_{1}^{\mathrm{new}}(795, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
795.1.x.a	$795$	$1$	795.x	795.x	$26$	$12$	$1$	$0.397$	\(\Q(\zeta_{26})\)	$D_{13}$	\(\Q(\sqrt{-15}) \)	None		✓			795.1.x.a	$4$	$0$	\(-2\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+(-\zeta_{26}^{7}+\zeta_{26}^{10})q^{2}+\zeta_{26}^{8}q^{3}+\cdots\)
795.1.x.b	$795$	$1$	795.x	795.x	$26$	$12$	$1$	$0.397$	\(\Q(\zeta_{26})\)	$D_{13}$	\(\Q(\sqrt{-15}) \)	None		✓			795.1.x.a	$4$	$0$	\(2\)	\(1\)	\(1\)	\(0\)	$1$		\(q+(\zeta_{26}^{7}-\zeta_{26}^{10})q^{2}-\zeta_{26}^{8}q^{3}+(-\zeta_{26}+\cdots)q^{4}+\cdots\)