Space of modular forms of level 816, weight 2, and Character 816.r

• Label: 816.2.r
• Level: $816$
• Weight: $2$
• Character orbit: 816.r
• Rep. character: $\chi_{816}(395,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $280$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 816 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(816, [\chi])\).

	Total	New	Old
Modular forms	296	296	0
Cusp forms	280	280	0
Eisenstein series	16	16	0

Trace form

280 * q - 4 * q^3 - 8 * q^4 + 2 * q^6 - 8 * q^7 + 2 * q^12 - 8 * q^13 + 24 * q^15 - 16 * q^16 + 4 * q^18 - 4 * q^21 + 16 * q^22 + 14 * q^24 - 248 * q^25 - 4 * q^27 + 8 * q^28 - 16 * q^30 - 16 * q^31 - 8 * q^33 - 8 * q^37 - 4 * q^39 + 28 * q^40 - 8 * q^42 + 16 * q^45 - 20 * q^46 - 34 * q^48 + 24 * q^51 - 32 * q^52 - 14 * q^54 - 16 * q^55 - 12 * q^57 - 12 * q^58 + 92 * q^60 + 24 * q^61 + 40 * q^63 - 32 * q^64 + 12 * q^66 - 8 * q^67 - 4 * q^69 + 64 * q^70 + 28 * q^72 + 4 * q^75 + 16 * q^76 - 92 * q^78 - 8 * q^81 - 20 * q^82 - 4 * q^84 + 20 * q^88 + 12 * q^90 - 16 * q^91 - 12 * q^93 - 24 * q^94 + 26 * q^96 - 8 * q^97 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(816, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
816.2.r.a	$816$	$2$	816.r	816.r	$4$	$4$	$2$	$6.516$	\(\Q(i, \sqrt{5})\)	None		✓			816.2.r.a	$2$	$0$	\(-4\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots\)
816.2.r.b	$816$	$2$	816.r	816.r	$4$	$4$	$2$	$6.516$	\(\Q(i, \sqrt{5})\)	None		✓			816.2.r.a	$2$	$0$	\(4\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
816.2.r.c	$816$	$2$	816.r	816.r	$4$	$272$	$136$	$6.516$		None		✓	✓		816.2.r.c	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$