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

• Label: 833.2.o
• Level: $833$
• Weight: $2$
• Character orbit: 833.o
• Rep. character: $\chi_{833}(30,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $224$
• Newform subspaces: $8$
• Sturm bound: $168$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(168\)
Trace bound:			\(4\)
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	368	256	112
Cusp forms	304	224	80
Eisenstein series	64	32	32

Trace form

224 * q + 2 * q^3 + 108 * q^4 + 4 * q^5 + 16 * q^6 + 10 * q^10 + 12 * q^11 - 24 * q^12 - 92 * q^16 + 6 * q^17 - 20 * q^18 + 32 * q^20 - 72 * q^22 - 20 * q^24 - 16 * q^27 - 16 * q^29 + 68 * q^30 - 2 * q^31 + 20 * q^33 + 48 * q^34 - 6 * q^37 + 36 * q^38 + 20 * q^39 - 60 * q^40 + 12 * q^41 - 2 * q^44 + 12 * q^45 - 56 * q^46 + 40 * q^47 - 68 * q^48 + 48 * q^50 + 30 * q^51 - 12 * q^52 - 4 * q^54 - 112 * q^55 - 56 * q^57 - 64 * q^58 + 32 * q^61 - 52 * q^62 - 112 * q^64 - 50 * q^65 + 40 * q^67 - 8 * q^68 + 32 * q^69 - 140 * q^71 + 44 * q^72 - 4 * q^73 - 64 * q^74 + 8 * q^75 - 228 * q^78 + 12 * q^79 - 26 * q^80 + 12 * q^81 + 32 * q^82 - 116 * q^85 + 8 * q^86 - 108 * q^88 + 48 * q^89 - 4 * q^90 + 96 * q^92 - 52 * q^95 + 20 * q^96 + 84 * q^97 - 60 * 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.o.a	$833$	$2$	833.o	119.n	$12$	$4$	$1$	$6.652$	\(\Q(\zeta_{12})\)	None		✓			833.2.g.a	$4$	$1$	\(0\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
833.2.o.b	$833$	$2$	833.o	119.n	$12$	$4$	$1$	$6.652$	\(\Q(\zeta_{12})\)	None		✓			833.2.g.a	$4$	$0$	\(0\)	\(4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots\)
833.2.o.c	$833$	$2$	833.o	119.n	$12$	$8$	$2$	$6.652$	8.0.303595776.1	None					119.2.n.a	$4$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{4}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
833.2.o.d	$833$	$2$	833.o	119.n	$12$	$32$	$8$	$6.652$		None					119.2.n.b	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
833.2.o.e	$833$	$2$	833.o	119.n	$12$	$32$	$8$	$6.652$		None		✓			833.2.g.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
833.2.o.f	$833$	$2$	833.o	119.n	$12$	$40$	$10$	$6.652$		None					119.2.g.a	$4$	$0$	\(0\)	\(-4\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
833.2.o.g	$833$	$2$	833.o	119.n	$12$	$40$	$10$	$6.652$		None					119.2.g.a	$4$	$0$	\(0\)	\(4\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
833.2.o.h	$833$	$2$	833.o	119.n	$12$	$64$	$16$	$6.652$		None		✓	✓		833.2.g.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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