Space of modular forms of level 435, weight 3, and Character 435.be

• Label: 435.3.be
• Level: $435$
• Weight: $3$
• Character orbit: 435.be
• Rep. character: $\chi_{435}(31,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $480$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	435.be (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(435, [\chi])\).

	Total	New	Old
Modular forms	1488	480	1008
Cusp forms	1392	480	912
Eisenstein series	96	0	96

Trace form

480 * q - 8 * q^2 + 72 * q^8 + 64 * q^11 + 24 * q^14 + 336 * q^16 - 72 * q^17 + 24 * q^18 - 24 * q^19 + 672 * q^22 + 264 * q^23 + 72 * q^24 + 400 * q^25 + 104 * q^26 + 8 * q^29 - 264 * q^31 - 896 * q^32 + 480 * q^36 - 520 * q^37 - 1120 * q^38 + 48 * q^39 - 56 * q^41 + 216 * q^43 + 360 * q^44 + 832 * q^46 + 856 * q^47 - 96 * q^48 - 64 * q^49 + 40 * q^50 + 672 * q^51 + 1064 * q^52 - 832 * q^53 - 80 * q^55 + 800 * q^56 + 120 * q^58 - 144 * q^59 - 184 * q^61 - 1960 * q^62 - 1656 * q^66 - 1120 * q^67 + 576 * q^68 - 1176 * q^69 - 120 * q^70 - 1568 * q^71 - 624 * q^72 + 344 * q^73 - 744 * q^74 - 776 * q^76 - 1240 * q^77 - 360 * q^78 + 544 * q^79 + 720 * q^81 - 160 * q^83 + 216 * q^84 + 120 * q^85 - 168 * q^87 + 944 * q^88 - 40 * q^89 - 216 * q^94 + 80 * q^95 - 560 * q^97 + 2648 * q^98 - 192 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(435, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
435.3.be.a	$435$	$3$	435.be	29.f	$28$	$480$	$40$	$11.853$		None		✓	✓	✓	435.3.be.a	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{3}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)