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

• Label: 456.2.bg
• Level: $456$
• Weight: $2$
• Character orbit: 456.bg
• Rep. character: $\chi_{456}(25,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $160$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bg (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
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	528	60	468
Cusp forms	432	60	372
Eisenstein series	96	0	96

Trace form

60 * q + 6 * q^13 - 12 * q^17 + 6 * q^19 + 6 * q^21 - 12 * q^25 + 6 * q^27 + 24 * q^29 + 12 * q^31 + 36 * q^35 + 60 * q^41 + 54 * q^43 - 18 * q^49 + 36 * q^53 + 36 * q^55 - 12 * q^57 - 24 * q^59 + 24 * q^61 - 12 * q^63 - 36 * q^65 - 66 * q^67 - 24 * q^69 - 108 * q^71 - 6 * q^73 - 84 * q^75 - 72 * q^77 - 120 * q^79 + 12 * q^85 - 36 * q^87 - 36 * q^89 - 36 * q^91 - 12 * q^93 + 60 * q^97 - 12 * 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.bg.a	$456$	$2$	456.bg	19.e	$9$	$12$	$2$	$3.641$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			456.2.bg.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{2}-\beta _{11})q^{3}-\beta _{1}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
456.2.bg.b	$456$	$2$	456.bg	19.e	$9$	$12$	$2$	$3.641$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			456.2.bg.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{4}q^{3}+(1+\beta _{6}+\beta _{9}+\beta _{11})q^{5}+\cdots\)
456.2.bg.c	$456$	$2$	456.bg	19.e	$9$	$18$	$3$	$3.641$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			456.2.bg.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{7}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
456.2.bg.d	$456$	$2$	456.bg	19.e	$9$	$18$	$3$	$3.641$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			456.2.bg.d	$2$	$0$	\(0\)	\(0\)	\(3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{9}q^{3}+(1+\beta _{5}-\beta _{6}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(456, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)