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

• Label: 465.2.t
• Level: $465$
• Weight: $2$
• Character orbit: 465.t
• Rep. character: $\chi_{465}(119,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 465 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	136	136	0
Cusp forms	120	120	0
Eisenstein series	16	16	0

Trace form

120 * q + 100 * q^4 - 18 * q^6 + 2 * q^9 - 10 * q^10 + 60 * q^16 - 4 * q^19 - 6 * q^21 - 60 * q^24 + 8 * q^25 - 36 * q^31 - 54 * q^34 + 22 * q^36 + 12 * q^39 - 36 * q^40 - 24 * q^45 + 24 * q^49 - 12 * q^51 + 12 * q^55 - 80 * q^64 - 36 * q^66 + 40 * q^69 - 56 * q^70 + 54 * q^75 - 74 * q^76 + 12 * q^79 + 6 * q^81 - 42 * q^84 + 36 * q^90 - 76 * q^94 - 144 * q^96 + 126 * q^99

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.t.a	$465$	$2$	465.t	465.t	$6$	$4$	$2$	$3.713$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		✓			465.2.t.a	$4$	$0$	\(-6\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2-\beta _{2})q^{2}+(2+\beta _{3})q^{3}+(3+3\beta _{2}+\cdots)q^{4}+\cdots\)
465.2.t.b	$465$	$2$	465.t	465.t	$6$	$4$	$2$	$3.713$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		✓			465.2.t.a	$4$	$0$	\(6\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1-\beta _{2})q^{2}+(-2-\beta _{3})q^{3}-3\beta _{2}q^{4}+\cdots\)
465.2.t.c	$465$	$2$	465.t	465.t	$6$	$8$	$4$	$3.713$	\(\Q(\sqrt{-2}, \sqrt{-3}, \sqrt{-5})\)	None		✓			465.2.t.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}-2\beta _{5})q^{2}+(-\beta _{5}-\beta _{7})q^{3}+\cdots\)
465.2.t.d	$465$	$2$	465.t	465.t	$6$	$104$	$52$	$3.713$		None		✓	✓		465.2.t.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$