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

• Label: 465.2.c
• Level: $465$
• Weight: $2$
• Character orbit: 465.c
• Rep. character: $\chi_{465}(94,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	68	32	36
Cusp forms	60	32	28
Eisenstein series	8	0	8

Trace form

32 * q - 36 * q^4 - 32 * q^9 - 2 * q^10 - 4 * q^14 + 4 * q^15 + 60 * q^16 - 16 * q^19 + 14 * q^20 - 12 * q^25 - 24 * q^26 + 8 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^34 + 36 * q^36 - 16 * q^39 - 8 * q^40 - 16 * q^41 + 40 * q^44 - 16 * q^46 - 24 * q^49 + 22 * q^50 + 8 * q^51 + 28 * q^55 - 48 * q^56 - 8 * q^59 - 12 * q^60 - 80 * q^64 + 44 * q^65 + 8 * q^66 - 16 * q^69 + 14 * q^70 - 24 * q^71 + 88 * q^74 - 8 * q^75 + 4 * q^76 + 32 * q^79 - 70 * q^80 + 32 * q^81 - 8 * q^84 - 8 * q^85 - 16 * q^86 + 8 * q^89 + 2 * q^90 - 8 * q^91 - 16 * q^94 + 16 * q^95 + 40 * q^96

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.c.a	$465$	$2$	465.c	5.b	$2$	$10$	$10$	$3.713$	10.0.\(\cdots\).1	None		✓			465.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{8})q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
465.2.c.b	$465$	$2$	465.c	5.b	$2$	$22$	$22$	$3.713$		None		✓	✓		465.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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