Space of modular forms of level 435, weight 4, and Character 435.d

• Label: 435.4.d
• Level: $435$
• Weight: $4$
• Character orbit: 435.d
• Rep. character: $\chi_{435}(376,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(435, [\chi])\).

	Total	New	Old
Modular forms	184	60	124
Cusp forms	176	60	116
Eisenstein series	8	0	8

Trace form

60 * q - 280 * q^4 - 56 * q^7 - 540 * q^9 + 104 * q^13 + 1400 * q^16 + 148 * q^22 + 944 * q^23 + 180 * q^24 + 1500 * q^25 - 180 * q^28 - 88 * q^29 - 120 * q^30 + 456 * q^33 + 516 * q^34 - 80 * q^35 + 2520 * q^36 - 1016 * q^38 + 708 * q^42 + 3324 * q^49 + 480 * q^51 - 1212 * q^52 + 400 * q^53 + 456 * q^57 - 364 * q^58 + 984 * q^59 + 3848 * q^62 + 504 * q^63 - 7748 * q^64 + 232 * q^67 - 5664 * q^71 + 1072 * q^74 - 4092 * q^78 + 1760 * q^80 + 4860 * q^81 + 4720 * q^82 - 4088 * q^83 + 7920 * q^86 + 984 * q^87 + 9824 * q^88 - 328 * q^91 - 10776 * q^92 - 72 * q^93 - 9740 * q^94 - 2040 * q^96

Decomposition of \(S_{4}^{\mathrm{new}}(435, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
435.4.d.a	$435$	$4$	435.d	29.b	$2$	$30$	$30$	$25.666$		None		✓			435.4.d.a	$2$	$0$	\(0\)	\(0\)	\(-150\)	\(-20\)		$\mathrm{SU}(2)[C_{2}]$
435.4.d.b	$435$	$4$	435.d	29.b	$2$	$30$	$30$	$25.666$		None		✓			435.4.d.b	$2$	$0$	\(0\)	\(0\)	\(150\)	\(-36\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)