Space of modular forms of level 330, weight 2, and Character 330.p

• Label: 330.2.p
• Level: $330$
• Weight: $2$
• Character orbit: 330.p
• Rep. character: $\chi_{330}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.p (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(330, [\chi])\).

	Total	New	Old
Modular forms	320	96	224
Cusp forms	256	96	160
Eisenstein series	64	0	64

Trace form

96 * q + 24 * q^4 + 8 * q^9 + 4 * q^15 - 24 * q^16 - 32 * q^25 - 30 * q^30 - 4 * q^31 + 8 * q^34 + 12 * q^36 + 20 * q^39 - 10 * q^40 + 48 * q^45 - 20 * q^46 - 144 * q^49 - 20 * q^51 - 24 * q^55 - 4 * q^60 - 40 * q^61 + 24 * q^64 + 44 * q^66 - 48 * q^69 + 22 * q^70 - 48 * q^75 - 20 * q^79 + 104 * q^81 - 20 * q^84 - 60 * q^85 - 90 * q^90 + 40 * q^91 - 80 * q^94 - 124 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(330, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
330.2.p.a	$330$	$2$	330.p	165.r	$10$	$96$	$24$	$2.635$		None		✓	✓	✓	330.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(330, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)