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

• Label: 465.2.bf
• Level: $465$
• Weight: $2$
• Character orbit: 465.bf
• Rep. character: $\chi_{465}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $128$
• 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.bf (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
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	128	144
Cusp forms	240	128	112
Eisenstein series	32	0	32

Trace form

128 * q + 12 * q^6 + 4 * q^7 - 24 * q^8 + 8 * q^10 - 168 * q^16 - 40 * q^20 + 24 * q^21 + 72 * q^22 - 8 * q^25 - 24 * q^28 - 16 * q^31 - 8 * q^32 - 24 * q^33 - 72 * q^35 + 68 * q^36 - 36 * q^37 + 48 * q^38 + 44 * q^40 + 8 * q^41 - 12 * q^42 + 72 * q^43 + 56 * q^47 + 32 * q^50 + 8 * q^51 - 108 * q^52 - 60 * q^55 + 80 * q^56 + 24 * q^57 + 40 * q^62 + 8 * q^63 - 108 * q^65 - 16 * q^66 - 40 * q^67 - 132 * q^68 - 32 * q^70 + 56 * q^71 + 12 * q^72 + 24 * q^73 + 52 * q^76 + 60 * q^80 + 64 * q^81 - 4 * q^82 - 132 * q^83 + 28 * q^87 - 156 * q^88 + 12 * q^90 - 32 * q^93 + 16 * q^95 + 84 * q^96 + 40 * q^97 + 64 * q^98

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.bf.a	$465$	$2$	465.bf	155.p	$12$	$128$	$32$	$3.713$		None		✓	✓	✓	465.2.bf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(465, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)