Space of modular forms of level 430, weight 2, and trivial character

• Label: 430.2.a
• Level: $430$
• Weight: $2$
• Character orbit: 430.a
• Rep. character: $\chi_{430}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $8$
• Sturm bound: $132$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(132\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(430))\).

	Total	New	Old
Modular forms	70	13	57
Cusp forms	63	13	50
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(43\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(2\)
Plus space			\(+\)	\(4\)
Minus space			\(-\)	\(9\)

Trace form

\( 13 q - q^{2} - 4 q^{3} + 13 q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 9 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(430))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	43
430.2.a.a	$430$	$2$	430.a	1.a	$1$	$1$	$1$	$3.434$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
430.2.a.b	$430$	$2$	430.a	1.a	$1$	$1$	$1$	$3.434$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-3q^{9}+\cdots\)
430.2.a.c	$430$	$2$	430.a	1.a	$1$	$1$	$1$	$3.434$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
430.2.a.d	$430$	$2$	430.a	1.a	$1$	$1$	$1$	$3.434$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(1\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}-5q^{7}+\cdots\)
430.2.a.e	$430$	$2$	430.a	1.a	$1$	$2$	$2$	$3.434$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
430.2.a.f	$430$	$2$	430.a	1.a	$1$	$2$	$2$	$3.434$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots\)
430.2.a.g	$430$	$2$	430.a	1.a	$1$	$2$	$2$	$3.434$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
430.2.a.h	$430$	$2$	430.a	1.a	$1$	$3$	$3$	$3.434$	3.3.316.1	None	✓	$1$	$0$	\(-3\)	\(-2\)	\(-3\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(430))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(430)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 2}\)