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

• Label: 456.2.bm
• Level: $456$
• Weight: $2$
• Character orbit: 456.bm
• Rep. character: $\chi_{456}(41,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bm (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
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	528	120	408
Cusp forms	432	120	312
Eisenstein series	96	0	96

Trace form

120 * q - 3 * q^3 - 9 * q^9 + 6 * q^13 - 12 * q^15 + 6 * q^19 + 12 * q^25 + 9 * q^27 + 45 * q^33 + 36 * q^39 - 42 * q^43 + 18 * q^45 - 60 * q^49 + 27 * q^51 + 36 * q^55 + 24 * q^57 - 12 * q^61 + 54 * q^63 - 96 * q^67 - 114 * q^73 - 72 * q^79 - 33 * q^81 + 12 * q^85 - 18 * q^87 - 36 * q^91 + 54 * q^93 + 30 * q^97 - 42 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
456.2.bm.a	$456$	$2$	456.bm	57.j	$18$	$60$	$10$	$3.641$		None		✓			456.2.bm.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
456.2.bm.b	$456$	$2$	456.bm	57.j	$18$	$60$	$10$	$3.641$		None		✓			456.2.bm.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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