Space of modular forms of level 456, weight 2, and Character 456.q

• Label: 456.2.q
• Level: $456$
• Weight: $2$
• Character orbit: 456.q
• Rep. character: $\chi_{456}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $6$
• Sturm bound: $160$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(160\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(456, [\chi])\).

	Total	New	Old
Modular forms	176	20	156
Cusp forms	144	20	124
Eisenstein series	32	0	32

Trace form

\( 20 q + 2 q^{3} + 4 q^{7} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(456, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
456.2.q.a	$456$	$2$	456.q	19.c	$3$	$2$	$1$	$3.641$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-1\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-3q^{7}+\cdots\)
456.2.q.b	$456$	$2$	456.q	19.c	$3$	$2$	$1$	$3.641$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots\)
456.2.q.c	$456$	$2$	456.q	19.c	$3$	$2$	$1$	$3.641$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-5q^{7}+\cdots\)
456.2.q.d	$456$	$2$	456.q	19.c	$3$	$4$	$2$	$3.641$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
456.2.q.e	$456$	$2$	456.q	19.c	$3$	$4$	$2$	$3.641$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
456.2.q.f	$456$	$2$	456.q	19.c	$3$	$6$	$3$	$3.641$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(6\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{18}q^{3}+\zeta_{18}^{2}q^{5}+(1+\zeta_{18}^{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)