Space of modular forms of level 678, weight 3, and Character 678.d

• Label: 678.3.d
• Level: $678$
• Weight: $3$
• Character orbit: 678.d
• Rep. character: $\chi_{678}(677,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $342$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 678 = 2 \cdot 3 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	678.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 339 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(342\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(678, [\chi])\).

	Total	New	Old
Modular forms	232	76	156
Cusp forms	224	76	148
Eisenstein series	8	0	8

Trace form

76 * q - 152 * q^4 - 24 * q^9 + 40 * q^13 + 28 * q^15 + 304 * q^16 - 48 * q^18 + 48 * q^22 + 476 * q^25 + 112 * q^30 - 104 * q^31 + 48 * q^36 + 516 * q^49 + 252 * q^51 - 80 * q^52 + 132 * q^57 - 56 * q^60 - 80 * q^61 + 216 * q^63 - 608 * q^64 + 356 * q^69 + 96 * q^72 + 240 * q^81 + 48 * q^82 + 316 * q^85 - 72 * q^87 - 96 * q^88 - 268 * q^91 + 180 * q^97 + 540 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(678, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
678.3.d.a	$678$	$3$	678.d	339.c	$2$	$76$	$76$	$18.474$		None		✓	✓	✓	678.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(678, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(678, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(339, [\chi])\)\(^{\oplus 2}\)