Space of modular forms of level 429, weight 2, and Character 429.n

• Label: 429.2.n
• Level: $429$
• Weight: $2$
• Character orbit: 429.n
• Rep. character: $\chi_{429}(157,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).

	Total	New	Old
Modular forms	240	96	144
Cusp forms	208	96	112
Eisenstein series	32	0	32

Trace form

96 * q + 8 * q^2 - 16 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^7 - 16 * q^8 - 24 * q^9 + 16 * q^10 + 12 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^15 - 52 * q^16 - 24 * q^17 - 12 * q^18 + 16 * q^19 + 32 * q^20 - 32 * q^21 + 28 * q^22 + 48 * q^23 + 12 * q^24 - 16 * q^25 + 20 * q^29 + 4 * q^30 - 24 * q^31 + 16 * q^32 + 16 * q^33 - 32 * q^34 - 40 * q^35 - 16 * q^36 - 36 * q^37 + 64 * q^38 + 8 * q^39 - 96 * q^40 - 4 * q^42 + 48 * q^43 - 128 * q^44 + 8 * q^45 - 44 * q^46 + 48 * q^47 - 24 * q^48 + 20 * q^49 - 76 * q^50 - 4 * q^51 - 16 * q^53 - 16 * q^54 - 56 * q^55 + 96 * q^56 + 64 * q^58 + 8 * q^59 + 24 * q^60 - 60 * q^62 + 4 * q^63 - 96 * q^64 + 36 * q^66 + 60 * q^68 + 16 * q^69 + 28 * q^70 + 8 * q^71 + 4 * q^72 - 28 * q^73 + 104 * q^74 - 8 * q^75 - 112 * q^76 - 16 * q^77 - 44 * q^79 - 156 * q^80 - 24 * q^81 + 84 * q^82 + 56 * q^83 + 44 * q^85 + 32 * q^86 + 16 * q^87 + 60 * q^88 + 56 * q^89 - 4 * q^90 + 8 * q^91 - 16 * q^92 - 56 * q^93 - 80 * q^94 - 60 * q^95 + 28 * q^96 + 104 * q^97 - 256 * q^98 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(429, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
429.2.n.a	$429$	$2$	429.n	11.c	$5$	$12$	$3$	$3.426$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			429.2.n.a	$2$	$0$	\(3\)	\(-3\)	\(8\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
429.2.n.b	$429$	$2$	429.n	11.c	$5$	$20$	$5$	$3.426$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			429.2.n.b	$2$	$0$	\(1\)	\(5\)	\(4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{2}-\beta _{9}q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
429.2.n.c	$429$	$2$	429.n	11.c	$5$	$28$	$7$	$3.426$		None		✓			429.2.n.c	$2$	$0$	\(1\)	\(7\)	\(-4\)	\(1\)		$\mathrm{SU}(2)[C_{5}]$
429.2.n.d	$429$	$2$	429.n	11.c	$5$	$36$	$9$	$3.426$		None		✓	✓		429.2.n.d	$2$	$0$	\(3\)	\(-9\)	\(0\)	\(1\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(429, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(429, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)