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

• Label: 456.2.bf
• Level: $456$
• Weight: $2$
• Character orbit: 456.bf
• Rep. character: $\chi_{456}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
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	40	136
Cusp forms	144	40	104
Eisenstein series	32	0	32

Trace form

\( 40 q + 3 q^{3} + 4 q^{7} + 3 q^{9} + O(q^{10}) \)

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.bf.a	$456$	$2$	456.bf	57.f	$6$	$4$	$2$	$3.641$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
456.2.bf.b	$456$	$2$	456.bf	57.f	$6$	$4$	$2$	$3.641$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(2\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots\)
456.2.bf.c	$456$	$2$	456.bf	57.f	$6$	$16$	$8$	$3.641$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}-\beta _{14}q^{5}+(\beta _{5}-\beta _{13})q^{7}+\cdots\)
456.2.bf.d	$456$	$2$	456.bf	57.f	$6$	$16$	$8$	$3.641$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(\beta _{5}-\beta _{13}+\cdots)q^{7}+\cdots\)

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

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