Space of modular forms of level 416, weight 3, and Character 416.j

• Label: 416.3.j
• Level: $416$
• Weight: $3$
• Character orbit: 416.j
• Rep. character: $\chi_{416}(177,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	416.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(416, [\chi])\).

	Total	New	Old
Modular forms	240	60	180
Cusp forms	208	52	156
Eisenstein series	32	8	24

Trace form

52 * q + 4 * q^7 - 140 * q^9 - 32 * q^15 + 4 * q^31 + 32 * q^33 - 32 * q^39 + 36 * q^41 + 4 * q^47 - 248 * q^55 - 64 * q^57 + 164 * q^63 + 52 * q^65 - 252 * q^71 - 284 * q^73 + 8 * q^79 + 244 * q^81 + 704 * q^87 - 204 * q^89 + 292 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(416, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
416.3.j.a	$416$	$3$	416.j	104.j	$4$	$52$	$26$	$11.335$		None			✓	✓	104.3.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(416, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(416, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)