Space of modular forms of level 465, weight 2, and Character 465.be

• Label: 465.2.be
• Level: $465$
• Weight: $2$
• Character orbit: 465.be
• Rep. character: $\chi_{465}(98,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 465 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(465, [\chi])\).

	Total	New	Old
Modular forms	272	272	0
Cusp forms	240	240	0
Eisenstein series	32	32	0

Trace form

240 * q - 6 * q^3 - 4 * q^6 + 4 * q^10 + 24 * q^12 - 4 * q^13 - 24 * q^15 - 216 * q^16 - 6 * q^18 - 4 * q^21 + 8 * q^22 + 48 * q^27 + 16 * q^28 + 60 * q^30 - 24 * q^31 - 4 * q^33 + 12 * q^36 + 12 * q^40 + 70 * q^42 - 4 * q^43 + 38 * q^45 - 96 * q^46 + 48 * q^48 + 4 * q^51 + 20 * q^52 - 52 * q^55 - 34 * q^57 - 104 * q^58 - 96 * q^60 + 16 * q^61 - 64 * q^63 - 208 * q^66 + 8 * q^67 + 96 * q^70 + 64 * q^72 + 12 * q^73 - 12 * q^75 - 12 * q^76 + 76 * q^78 + 12 * q^81 + 52 * q^82 - 56 * q^85 + 22 * q^87 + 48 * q^88 - 80 * q^91 + 6 * q^93 - 68 * q^96 - 144 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(465, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
465.2.be.a	$465$	$2$	465.be	465.ae	$12$	$240$	$60$	$3.713$		None		✓	✓	✓	465.2.be.a	$8$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$