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

• Label: 465.2.i
• Level: $465$
• Weight: $2$
• Character orbit: 465.i
• Rep. character: $\chi_{465}(211,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $44$
• Newform subspaces: $6$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	136	44	92
Cusp forms	120	44	76
Eisenstein series	16	0	16

Trace form

44 * q + 2 * q^3 + 52 * q^4 - 2 * q^6 + 4 * q^7 - 22 * q^9 - 2 * q^10 - 4 * q^11 + 4 * q^12 + 10 * q^13 + 8 * q^14 - 8 * q^15 + 84 * q^16 + 12 * q^17 - 6 * q^19 - 8 * q^20 + 12 * q^21 - 48 * q^23 - 22 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 - 8 * q^30 - 12 * q^31 + 40 * q^32 - 16 * q^33 - 30 * q^34 - 16 * q^35 - 26 * q^36 - 6 * q^37 - 44 * q^38 - 4 * q^39 + 8 * q^41 + 8 * q^42 + 34 * q^43 - 44 * q^44 + 8 * q^48 + 2 * q^49 - 16 * q^51 + 24 * q^52 - 36 * q^53 + 4 * q^54 + 12 * q^55 - 28 * q^56 + 2 * q^57 - 128 * q^58 + 4 * q^59 - 12 * q^60 + 16 * q^61 - 8 * q^63 + 24 * q^64 + 24 * q^66 + 16 * q^67 - 20 * q^68 + 16 * q^69 + 16 * q^70 + 20 * q^71 - 6 * q^73 - 20 * q^74 + 2 * q^75 + 2 * q^76 + 48 * q^77 + 56 * q^78 - 24 * q^79 - 16 * q^80 - 22 * q^81 - 20 * q^82 + 12 * q^83 + 8 * q^85 - 36 * q^86 - 4 * q^87 - 4 * q^88 - 2 * q^90 - 72 * q^91 - 40 * q^92 + 14 * q^93 + 60 * q^94 - 22 * q^96 + 36 * q^97 - 32 * q^98 - 4 * 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.i.a	$465$	$2$	465.i	31.c	$3$	$2$	$1$	$3.713$	\(\Q(\sqrt{-3}) \)	None		✓			465.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
465.2.i.b	$465$	$2$	465.i	31.c	$3$	$4$	$2$	$3.713$	\(\Q(\sqrt{-3}, \sqrt{97})\)	None		✓			465.2.i.b	$2$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{3}-2q^{4}+\beta _{2}q^{5}-\beta _{2}q^{9}+\cdots\)
465.2.i.c	$465$	$2$	465.i	31.c	$3$	$6$	$3$	$3.713$	6.0.309123.1	None		✓			465.2.i.c	$2$	$0$	\(-4\)	\(3\)	\(3\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}+(1-\beta _{4})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
465.2.i.d	$465$	$2$	465.i	31.c	$3$	$8$	$4$	$3.713$	8.0.\(\cdots\).1	None		✓			465.2.i.d	$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{6}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
465.2.i.e	$465$	$2$	465.i	31.c	$3$	$10$	$5$	$3.713$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			465.2.i.e	$2$	$0$	\(2\)	\(-5\)	\(5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
465.2.i.f	$465$	$2$	465.i	31.c	$3$	$14$	$7$	$3.713$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓		465.2.i.f	$2$	$0$	\(2\)	\(7\)	\(-7\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{3})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(465, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)