Space of modular forms of level 770, weight 2, and Character 770.bm

• Label: 770.2.bm
• Level: $770$
• Weight: $2$
• Character orbit: 770.bm
• Rep. character: $\chi_{770}(61,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $256$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bm (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

	Total	New	Old
Modular forms	1216	256	960
Cusp forms	1088	256	832
Eisenstein series	128	0	128

Trace form

256 * q - 32 * q^4 - 44 * q^9 + 6 * q^11 - 2 * q^14 + 24 * q^15 + 32 * q^16 + 60 * q^17 + 8 * q^22 + 24 * q^23 - 32 * q^25 + 60 * q^26 - 40 * q^29 + 24 * q^33 - 48 * q^36 + 8 * q^37 + 24 * q^38 - 20 * q^39 - 40 * q^42 - 6 * q^44 + 24 * q^47 + 60 * q^49 + 60 * q^51 + 24 * q^53 + 8 * q^58 + 120 * q^59 - 8 * q^60 - 200 * q^63 + 64 * q^64 + 48 * q^66 - 32 * q^67 - 60 * q^68 + 128 * q^71 - 40 * q^72 - 180 * q^73 - 40 * q^74 - 60 * q^77 - 192 * q^78 - 60 * q^79 + 60 * q^81 - 72 * q^82 - 80 * q^84 + 16 * q^86 - 16 * q^88 - 48 * q^89 - 98 * q^91 - 72 * q^92 - 100 * q^93 + 90 * q^94 - 116 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
770.2.bm.a	$770$	$2$	770.bm	77.n	$30$	$128$	$16$	$6.148$		None		✓			770.2.bm.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$
770.2.bm.b	$770$	$2$	770.bm	77.n	$30$	$128$	$16$	$6.148$		None		✓			770.2.bm.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)