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

• Label: 456.2.p
• Level: $456$
• Weight: $2$
• Character orbit: 456.p
• Rep. character: $\chi_{456}(341,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	84	84	0
Cusp forms	76	76	0
Eisenstein series	8	8	0

Trace form

76 * q - 8 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^9 - 8 * q^16 - 2 * q^24 + 52 * q^25 - 20 * q^28 - 38 * q^36 - 16 * q^39 + 38 * q^42 + 60 * q^49 + 32 * q^54 - 48 * q^55 - 12 * q^57 + 12 * q^58 - 32 * q^63 - 32 * q^64 - 12 * q^66 - 24 * q^73 - 60 * q^76 - 12 * q^81 - 40 * q^82 - 48 * q^87 - 6 * q^96

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.p.a	$456$	$2$	456.p	456.p	$2$	$12$	$12$	$3.641$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	\(\Q(\sqrt{-38}) \)		✓			456.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+\beta _{8}q^{3}-2q^{4}-\beta _{2}q^{6}+(\beta _{10}+\cdots)q^{7}+\cdots\)
456.2.p.b	$456$	$2$	456.p	456.p	$2$	$64$	$64$	$3.641$		None		✓	✓		456.2.p.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$