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

• Label: 429.2.b
• Level: $429$
• Weight: $2$
• Character orbit: 429.b
• Rep. character: $\chi_{429}(298,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
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	60	24	36
Cusp forms	52	24	28
Eisenstein series	8	0	8

Trace form

\( 24 q + 4 q^{3} - 24 q^{4} + 24 q^{9} + O(q^{10}) \)

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.b.a	$429$	$2$	429.b	13.b	$2$	$10$	$10$	$3.426$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
429.2.b.b	$429$	$2$	429.b	13.b	$2$	$14$	$14$	$3.426$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1-\beta _{5}+\beta _{6})q^{4}+\cdots\)

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

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