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

• Label: 429.2.y
• Level: $429$
• Weight: $2$
• Character orbit: 429.y
• Rep. character: $\chi_{429}(116,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $208$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.y (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 429 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
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	240	0
Cusp forms	208	208	0
Eisenstein series	32	32	0

Trace form

\( 208 q - 6 q^{3} + 36 q^{4} - 18 q^{9} + O(q^{10}) \)

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.y.a	$429$	$2$	429.y	429.y	$10$	$32$	$8$	$3.426$		\(\Q(\sqrt{-39}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{10}]$
429.2.y.b	$429$	$2$	429.y	429.y	$10$	$176$	$44$	$3.426$		None		$8$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$