Space of modular forms of level 783, weight 2, and Character 783.v

• Label: 783.2.v
• Level: $783$
• Weight: $2$
• Character orbit: 783.v
• Rep. character: $\chi_{783}(26,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $180$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.v (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(180\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(783, [\chi])\).

	Total	New	Old
Modular forms	1152	480	672
Cusp forms	1008	480	528
Eisenstein series	144	0	144

Trace form

480 * q - 12 * q^10 + 144 * q^16 + 4 * q^19 - 80 * q^25 - 8 * q^31 - 52 * q^37 + 52 * q^40 - 8 * q^43 - 160 * q^46 - 64 * q^49 + 124 * q^52 - 208 * q^55 + 64 * q^58 + 84 * q^61 + 56 * q^67 + 104 * q^70 - 104 * q^73 - 68 * q^76 - 48 * q^79 + 8 * q^82 - 4 * q^85 - 232 * q^88 - 84 * q^91 + 4 * q^94 + 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(783, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
783.2.v.a	$783$	$2$	783.v	87.k	$28$	$240$	$20$	$6.252$		None		✓			783.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$
783.2.v.b	$783$	$2$	783.v	87.k	$28$	$240$	$20$	$6.252$		None		✓			783.2.v.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{2}^{\mathrm{old}}(783, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(783, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)