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

• Label: 429.2.be
• Level: $429$
• Weight: $2$
• Character orbit: 429.be
• Rep. character: $\chi_{429}(89,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	240	184	56
Cusp forms	208	184	24
Eisenstein series	32	0	32

Trace form

184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

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.be.a	$429$	$2$	429.be	39.k	$12$	$184$	$46$	$3.426$		None		✓	✓	✓	429.2.be.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)