Space of modular forms of level 385, weight 2, and Character 385.bl

• Label: 385.2.bl
• Level: $385$
• Weight: $2$
• Character orbit: 385.bl
• Rep. character: $\chi_{385}(61,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $256$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.bl (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

	Total	New	Old
Modular forms	416	256	160
Cusp forms	352	256	96
Eisenstein series	64	0	64

Trace form

256 * q - 28 * q^4 - 40 * q^8 - 26 * q^9 + 10 * q^14 - 12 * q^15 + 68 * q^16 - 60 * q^17 - 50 * q^18 + 104 * q^22 - 20 * q^23 - 180 * q^24 - 32 * q^25 - 60 * q^26 + 40 * q^29 - 24 * q^33 - 16 * q^36 - 32 * q^37 - 84 * q^38 + 40 * q^39 - 48 * q^42 - 22 * q^44 + 10 * q^46 - 12 * q^47 - 72 * q^49 - 60 * q^51 - 20 * q^53 - 12 * q^56 - 34 * q^58 - 36 * q^59 - 26 * q^60 + 140 * q^63 + 80 * q^64 - 12 * q^66 - 24 * q^67 + 180 * q^68 + 44 * q^70 - 128 * q^71 + 170 * q^72 + 90 * q^73 - 30 * q^74 - 44 * q^77 + 80 * q^78 + 130 * q^79 + 24 * q^80 - 2 * q^81 + 216 * q^82 + 120 * q^84 + 74 * q^86 - 104 * q^88 - 2 * q^91 + 60 * q^92 + 98 * q^93 - 90 * q^94 - 210 * q^96 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
385.2.bl.a	$385$	$2$	385.bl	77.n	$30$	$256$	$32$	$3.074$		None		✓	✓	✓	385.2.bl.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(385, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)