Space of modular forms of level 416, weight 4, and Character 416.z

• Label: 416.4.z
• Level: $416$
• Weight: $4$
• Character orbit: 416.z
• Rep. character: $\chi_{416}(81,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	416.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(416, [\chi])\).

	Total	New	Old
Modular forms	352	88	264
Cusp forms	320	80	240
Eisenstein series	32	8	24

Trace form

80 * q + 2 * q^7 + 322 * q^9 - 52 * q^15 - 28 * q^17 - 274 * q^23 - 1564 * q^25 + 8 * q^31 - 110 * q^33 + 658 * q^39 - 120 * q^41 + 8 * q^47 - 1734 * q^49 - 1272 * q^55 + 556 * q^57 - 1424 * q^63 + 410 * q^65 + 226 * q^71 + 1164 * q^73 - 3152 * q^79 - 1892 * q^81 - 4006 * q^87 - 222 * q^89 + 3412 * q^95 - 118 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(416, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
416.4.z.a	$416$	$4$	416.z	104.r	$6$	$80$	$40$	$24.545$		None			✓	✓	104.4.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(416, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(416, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)