Space of modular forms of level 435, weight 2, and Character 435.u

• Label: 435.2.u
• Level: $435$
• Weight: $2$
• Character orbit: 435.u
• Rep. character: $\chi_{435}(16,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.u (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).

	Total	New	Old
Modular forms	384	120	264
Cusp forms	336	120	216
Eisenstein series	48	0	48

Trace form

120 * q + 8 * q^2 - 12 * q^4 + 8 * q^7 + 24 * q^8 - 20 * q^9 - 40 * q^11 + 8 * q^13 + 24 * q^14 - 52 * q^16 + 24 * q^17 + 8 * q^18 + 8 * q^19 - 32 * q^22 + 12 * q^23 + 12 * q^24 - 20 * q^25 + 56 * q^26 - 120 * q^28 + 4 * q^29 - 24 * q^30 + 12 * q^31 - 156 * q^32 + 16 * q^33 + 36 * q^34 + 8 * q^35 - 12 * q^36 + 36 * q^37 + 16 * q^38 + 8 * q^39 + 8 * q^41 + 36 * q^42 + 40 * q^43 + 20 * q^44 + 56 * q^46 - 72 * q^47 + 32 * q^48 - 20 * q^49 + 8 * q^50 - 60 * q^51 - 44 * q^52 + 96 * q^53 - 20 * q^55 - 56 * q^56 - 48 * q^57 + 28 * q^58 - 16 * q^59 + 16 * q^61 - 116 * q^62 + 8 * q^63 + 16 * q^64 - 116 * q^66 - 32 * q^67 + 8 * q^68 - 32 * q^69 + 24 * q^70 - 44 * q^71 - 4 * q^72 + 36 * q^73 + 28 * q^74 + 76 * q^76 + 80 * q^77 + 76 * q^78 - 36 * q^79 + 32 * q^80 - 20 * q^81 - 108 * q^82 - 16 * q^83 + 24 * q^84 + 8 * q^85 + 208 * q^86 + 16 * q^87 - 64 * q^88 + 60 * q^89 + 112 * q^91 + 44 * q^92 + 24 * q^93 + 76 * q^94 + 16 * q^95 - 76 * q^96 + 60 * q^97 + 52 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
435.2.u.a	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		None		✓			435.2.u.a	$2$	$0$	\(1\)	\(-5\)	\(5\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$
435.2.u.b	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		None		✓			435.2.u.b	$2$	$0$	\(1\)	\(5\)	\(-5\)	\(4\)		$\mathrm{SU}(2)[C_{7}]$
435.2.u.c	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		None		✓			435.2.u.c	$2$	$0$	\(3\)	\(-5\)	\(-5\)	\(4\)		$\mathrm{SU}(2)[C_{7}]$
435.2.u.d	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		None		✓			435.2.u.d	$2$	$0$	\(3\)	\(5\)	\(5\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

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