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

• Label: 429.2.m
• Level: $429$
• Weight: $2$
• Character orbit: 429.m
• Rep. character: $\chi_{429}(109,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 143 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	120	56	64
Cusp forms	104	56	48
Eisenstein series	16	0	16

Trace form

\( 56 q + 56 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
429.2.m.a	$429$	$2$	429.m	143.g	$4$	$28$	$14$	$3.426$		None		$4$	$0$	\(0\)	\(-28\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
429.2.m.b	$429$	$2$	429.m	143.g	$4$	$28$	$14$	$3.426$		None		$4$	$0$	\(0\)	\(28\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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