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

• Label: 456.2.bu
• Level: $456$
• Weight: $2$
• Character orbit: 456.bu
• Rep. character: $\chi_{456}(35,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $456$
• Newform subspaces: $3$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bu (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	504	504	0
Cusp forms	456	456	0
Eisenstein series	48	48	0

Trace form

\( 456 q - 12 q^{3} - 6 q^{4} - 6 q^{6} - 12 q^{9} + O(q^{10}) \)

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.bu.a	$456$	$2$	456.bu	456.au	$18$	$12$	$2$	$3.641$	12.0.\(\cdots\).1	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q-\beta _{11}q^{2}+(-\beta _{1}+\beta _{10})q^{3}-2\beta _{4}q^{4}+\cdots\)
456.2.bu.b	$456$	$2$	456.bu	456.au	$18$	$12$	$2$	$3.641$	12.0.\(\cdots\).1	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{9})q^{3}-2\beta _{4}q^{4}+\cdots\)
456.2.bu.c	$456$	$2$	456.bu	456.au	$18$	$432$	$72$	$3.641$		None		$8$	$0$	\(0\)	\(-18\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$