Space of modular forms of level 432, weight 2, and trivial character

• Label: 432.2.a
• Level: $432$
• Weight: $2$
• Character orbit: 432.a
• Rep. character: $\chi_{432}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $8$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(432))\).

	Total	New	Old
Modular forms	90	8	82
Cusp forms	55	8	47
Eisenstein series	35	0	35

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

\(2\)	\(3\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(2\)
\(-\)	\(-\)	\(+\)	\(2\)
Plus space		\(+\)	\(3\)
Minus space		\(-\)	\(5\)

Trace form

\( 8 q - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(432))\) 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	3
432.2.a.a	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+3q^{7}+4q^{11}+q^{13}+4q^{17}+\cdots\)
432.2.a.b	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}-3q^{11}-4q^{13}-2q^{19}+\cdots\)
432.2.a.c	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-5q^{11}+4q^{13}-8q^{17}+\cdots\)
432.2.a.d	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-5\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-5q^{7}-7q^{13}+q^{19}-5q^{25}+4q^{31}+\cdots\)
432.2.a.e	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+q^{7}+5q^{13}+7q^{19}-5q^{25}+4q^{31}+\cdots\)
432.2.a.f	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}+5q^{11}+4q^{13}+8q^{17}+\cdots\)
432.2.a.g	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}+3q^{11}-4q^{13}-2q^{19}+\cdots\)
432.2.a.h	$432$	$2$	432.a	1.a	$1$	$1$	$1$	$3.450$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+3q^{7}-4q^{11}+q^{13}-4q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(432))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(432)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 2}\)