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

• Label: 465.2.ba
• Level: $465$
• Weight: $2$
• Character orbit: 465.ba
• Rep. character: $\chi_{465}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• 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.ba (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{10})\)
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 + 36 * q^4 - 20 * q^6 + 32 * q^9 + 2 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 - 4 * q^19 + 36 * q^20 + 20 * q^21 - 20 * q^24 + 12 * q^25 + 24 * q^26 - 28 * q^29 - 8 * q^30 - 12 * q^31 - 44 * q^34 + 124 * q^36 - 4 * q^39 - 22 * q^40 + 36 * q^41 - 80 * q^44 + 46 * q^46 + 64 * q^49 + 68 * q^50 - 8 * q^51 - 10 * q^54 + 12 * q^55 - 432 * q^56 + 88 * q^59 + 12 * q^60 - 120 * q^61 + 40 * q^64 - 4 * q^65 + 12 * q^66 - 24 * q^69 - 74 * q^70 + 44 * q^71 + 132 * q^74 - 12 * q^75 - 14 * q^76 - 132 * q^79 + 70 * q^80 - 32 * q^81 + 8 * q^84 + 48 * q^85 - 104 * q^86 + 52 * q^89 - 2 * q^90 - 32 * q^91 - 204 * q^94 + 34 * q^95 - 20 * 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.ba.a	$465$	$2$	465.ba	155.n	$10$	$128$	$32$	$3.713$		None		✓	✓	✓	465.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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