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

• Label: 385.2.t
• Level: $385$
• Weight: $2$
• Character orbit: 385.t
• Rep. character: $\chi_{385}(144,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	104	80	24
Cusp forms	88	80	8
Eisenstein series	16	0	16

Trace form

80 * q + 40 * q^4 - 8 * q^6 + 36 * q^9 - 6 * q^10 - 28 * q^14 - 28 * q^15 - 36 * q^16 - 8 * q^19 - 24 * q^20 - 12 * q^24 + 4 * q^25 + 16 * q^26 + 48 * q^29 - 16 * q^30 + 12 * q^31 - 24 * q^34 + 14 * q^35 - 24 * q^36 - 24 * q^39 + 64 * q^40 + 8 * q^41 - 4 * q^44 + 6 * q^45 - 28 * q^46 + 24 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^54 + 48 * q^56 - 44 * q^59 - 36 * q^60 + 20 * q^61 - 40 * q^64 - 18 * q^65 + 16 * q^66 - 32 * q^69 + 6 * q^70 + 16 * q^71 - 24 * q^74 - 12 * q^75 + 56 * q^76 - 32 * q^79 - 50 * q^80 + 48 * q^81 - 156 * q^84 - 24 * q^85 + 76 * q^86 - 84 * q^89 - 188 * q^90 + 80 * q^91 + 56 * q^94 - 16 * q^95 - 84 * q^96

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.t.a	$385$	$2$	385.t	35.j	$6$	$4$	$2$	$3.074$	\(\Q(\zeta_{12})\)	None		✓			385.2.t.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
385.2.t.b	$385$	$2$	385.t	35.j	$6$	$36$	$18$	$3.074$		None		✓			385.2.t.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
385.2.t.c	$385$	$2$	385.t	35.j	$6$	$40$	$20$	$3.074$		None		✓	✓		385.2.t.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(385, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)