Space of modular forms of level 304, weight 3, and Character 304.bf

• Label: 304.3.bf
• Level: $304$
• Weight: $3$
• Character orbit: 304.bf
• Rep. character: $\chi_{304}(47,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $120$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	304.bf (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(304, [\chi])\).

	Total	New	Old
Modular forms	516	120	396
Cusp forms	444	120	324
Eisenstein series	72	0	72

Trace form

\( 120 q - 36 q^{9} + 24 q^{13} - 72 q^{21} - 180 q^{33} + 36 q^{41} + 420 q^{49} + 72 q^{53} + 120 q^{61} + 360 q^{65} + 96 q^{73} - 144 q^{77} - 396 q^{81} + 144 q^{85} - 1080 q^{89} - 432 q^{93} - 324 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(304, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.3.bf.a	$304$	$3$	304.bf	76.l	$18$	$36$	$6$	$8.283$		None		✓			304.3.bf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
304.3.bf.b	$304$	$3$	304.bf	76.l	$18$	$42$	$7$	$8.283$		None		✓			304.3.bf.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-27\)		$\mathrm{SU}(2)[C_{18}]$
304.3.bf.c	$304$	$3$	304.bf	76.l	$18$	$42$	$7$	$8.283$		None		✓			304.3.bf.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(27\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(304, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)