Space of modular forms of level 833, weight 2, and Character 833.t

• Label: 833.2.t
• Level: $833$
• Weight: $2$
• Character orbit: 833.t
• Rep. character: $\chi_{833}(48,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $448$
• Newform subspaces: $5$
• Sturm bound: $168$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.t (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(168\)
Trace bound:			\(12\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(833, [\chi])\).

	Total	New	Old
Modular forms	736	512	224
Cusp forms	608	448	160
Eisenstein series	128	64	64

Trace form

448 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 + 16 * q^15 - 32 * q^18 + 16 * q^23 - 32 * q^29 - 112 * q^30 + 80 * q^32 - 48 * q^37 - 16 * q^39 - 32 * q^43 + 80 * q^44 - 48 * q^46 + 80 * q^51 - 48 * q^53 - 32 * q^57 + 80 * q^58 - 112 * q^60 - 96 * q^64 + 48 * q^65 - 64 * q^71 - 112 * q^72 - 80 * q^74 - 160 * q^78 + 16 * q^79 + 112 * q^81 - 192 * q^85 - 128 * q^86 + 208 * q^88 - 416 * q^92 - 112 * q^93 + 80 * q^95 + 160 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(833, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
833.2.t.a	$833$	$2$	833.t	119.p	$16$	$72$	$9$	$6.652$		None		✓			833.2.t.a	$2$	$0$	\(0\)	\(-8\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
833.2.t.b	$833$	$2$	833.t	119.p	$16$	$72$	$9$	$6.652$		None		✓			833.2.t.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
833.2.t.c	$833$	$2$	833.t	119.p	$16$	$72$	$9$	$6.652$		None		✓			833.2.t.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
833.2.t.d	$833$	$2$	833.t	119.p	$16$	$72$	$9$	$6.652$		None		✓			833.2.t.a	$2$	$0$	\(0\)	\(8\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
833.2.t.e	$833$	$2$	833.t	119.p	$16$	$160$	$20$	$6.652$		None			✓		119.2.s.a	$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(833, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(833, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)