Space of modular forms of level 795, weight 2, and Character 795.m

• Label: 795.2.m
• Level: $795$
• Weight: $2$
• Character orbit: 795.m
• Rep. character: $\chi_{795}(158,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $208$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 795 = 3 \cdot 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	795.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 795 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(795, [\chi])\).

	Total	New	Old
Modular forms	224	224	0
Cusp forms	208	208	0
Eisenstein series	16	16	0

Trace form

208 * q - 8 * q^6 - 24 * q^13 - 8 * q^15 - 208 * q^16 + 16 * q^25 + 16 * q^28 + 56 * q^36 - 32 * q^37 + 52 * q^40 + 16 * q^42 - 8 * q^43 - 64 * q^46 - 20 * q^52 - 28 * q^57 - 36 * q^60 + 52 * q^63 + 72 * q^66 + 12 * q^70 + 68 * q^78 - 64 * q^81 + 52 * q^82 + 32 * q^90 + 32 * q^91 + 108 * q^93 + 80 * q^96 - 120 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(795, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
795.2.m.a	$795$	$2$	795.m	795.m	$4$	$40$	$20$	$6.348$		\(\Q(\sqrt{-159}) \)		✓			795.2.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{4}]$
795.2.m.b	$795$	$2$	795.m	795.m	$4$	$168$	$84$	$6.348$		None		✓	✓		795.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$