Space of modular forms of level 430, weight 2, and Character 430.e

• Label: 430.2.e
• Level: $430$
• Weight: $2$
• Character orbit: 430.e
• Rep. character: $\chi_{430}(221,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $132$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(132\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(430, [\chi])\).

	Total	New	Old
Modular forms	140	32	108
Cusp forms	124	32	92
Eisenstein series	16	0	16

Trace form

\( 32 q - 4 q^{2} + 4 q^{3} + 32 q^{4} + 2 q^{5} + 2 q^{6} + 8 q^{7} - 4 q^{8} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(430, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
430.2.e.a	$430$	$2$	430.e	43.c	$3$	$2$	$1$	$3.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(-3\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
430.2.e.b	$430$	$2$	430.e	43.c	$3$	$2$	$1$	$3.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
430.2.e.c	$430$	$2$	430.e	43.c	$3$	$2$	$1$	$3.434$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+q^{4}+(1-\zeta_{6})q^{5}-4\zeta_{6}q^{7}+\cdots\)
430.2.e.d	$430$	$2$	430.e	43.c	$3$	$4$	$2$	$3.434$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$2$	$0$	\(-4\)	\(4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-2\beta _{2}q^{3}+q^{4}+\beta _{2}q^{5}+2\beta _{2}q^{6}+\cdots\)
430.2.e.e	$430$	$2$	430.e	43.c	$3$	$6$	$3$	$3.434$	6.0.954288.1	None		$2$	$0$	\(6\)	\(1\)	\(3\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta _{4}+\beta _{5})q^{3}+q^{4}+\beta _{3}q^{5}+\cdots\)
430.2.e.f	$430$	$2$	430.e	43.c	$3$	$6$	$3$	$3.434$	6.0.27870912.1	None		$2$	$0$	\(6\)	\(2\)	\(-3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots\)
430.2.e.g	$430$	$2$	430.e	43.c	$3$	$10$	$5$	$3.434$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-10\)	\(1\)	\(5\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{5})q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(430, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(430, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 2}\)