Space of modular forms of level 414, weight 4, and Character 414.d

• Label: 414.4.d
• Level: $414$
• Weight: $4$
• Character orbit: 414.d
• Rep. character: $\chi_{414}(413,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	414.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(414, [\chi])\).

	Total	New	Old
Modular forms	224	24	200
Cusp forms	208	24	184
Eisenstein series	16	0	16

Trace form

24 * q - 96 * q^4 - 192 * q^13 + 384 * q^16 + 360 * q^25 - 432 * q^31 - 816 * q^46 + 216 * q^49 + 768 * q^52 - 1536 * q^55 - 1632 * q^58 - 1536 * q^64 - 2688 * q^70 + 3072 * q^73 - 2688 * q^82 - 5712 * q^85 + 3744 * q^94

Decomposition of \(S_{4}^{\mathrm{new}}(414, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
414.4.d.a	$414$	$4$	414.d	69.c	$2$	$24$	$24$	$24.427$		None		✓	✓	✓	414.4.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)