Space of modular forms of level 315, weight 3, and Character 315.bw

• Label: 315.3.bw
• Level: $315$
• Weight: $3$
• Character orbit: 315.bw
• Rep. character: $\chi_{315}(47,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $368$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.bw (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(315, [\chi])\).

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

368 * q - 6 * q^2 - 6 * q^3 - 12 * q^5 - 2 * q^7 - 12 * q^10 - 6 * q^12 - 2 * q^15 + 644 * q^16 - 54 * q^17 - 50 * q^18 + 72 * q^21 + 12 * q^22 - 4 * q^25 - 72 * q^27 + 16 * q^28 - 140 * q^30 - 12 * q^31 + 78 * q^32 + 24 * q^33 - 176 * q^36 - 4 * q^37 - 12 * q^38 - 144 * q^41 - 166 * q^42 - 4 * q^43 - 204 * q^45 - 32 * q^46 - 6 * q^47 - 18 * q^48 + 276 * q^50 + 20 * q^51 + 240 * q^56 + 104 * q^57 + 124 * q^58 - 310 * q^60 - 300 * q^61 - 912 * q^62 - 198 * q^63 + 426 * q^65 + 420 * q^66 + 2 * q^67 + 852 * q^68 + 198 * q^70 - 662 * q^72 - 12 * q^73 - 6 * q^75 - 192 * q^76 - 582 * q^77 + 94 * q^78 - 96 * q^80 + 8 * q^81 + 12 * q^82 - 4 * q^85 + 48 * q^87 + 156 * q^88 - 576 * q^90 - 16 * q^91 - 852 * q^92 + 244 * q^93 + 294 * q^95 - 684 * q^96 + 24 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(315, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.3.bw.a	$315$	$3$	315.bw	315.aw	$12$	$368$	$92$	$8.583$		None		✓	✓	✓	315.3.bu.a	$4$	$0$	\(-6\)	\(-6\)	\(-12\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$