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

• Label: 833.2.u
• Level: $833$
• Weight: $2$
• Character orbit: 833.u
• Rep. character: $\chi_{833}(86,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $888$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.u (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	1032	888	144
Cusp forms	984	888	96
Eisenstein series	48	0	48

Trace form

888 * q + 2 * q^3 + 72 * q^4 + 4 * q^5 - 28 * q^6 + 2 * q^7 + 12 * q^8 + 40 * q^9 - 6 * q^10 - 4 * q^11 + 4 * q^12 + 16 * q^13 + 2 * q^14 - 20 * q^15 + 68 * q^16 + 4 * q^17 - 4 * q^18 - 6 * q^19 - 48 * q^20 - 20 * q^22 + 58 * q^25 - 36 * q^26 - 16 * q^27 + 18 * q^28 - 60 * q^29 - 4 * q^30 - 78 * q^31 - 96 * q^32 - 26 * q^33 - 8 * q^34 - 10 * q^35 - 148 * q^36 - 48 * q^37 - 30 * q^38 + 6 * q^39 + 136 * q^40 + 12 * q^41 - 92 * q^42 + 12 * q^43 + 134 * q^44 - 178 * q^45 + 132 * q^46 - 16 * q^47 + 60 * q^48 + 16 * q^49 - 164 * q^50 + 114 * q^52 - 58 * q^53 + 196 * q^54 - 126 * q^55 + 94 * q^56 + 64 * q^57 - 128 * q^58 - 30 * q^59 - 88 * q^60 - 42 * q^61 - 36 * q^62 - 80 * q^63 - 84 * q^64 - 30 * q^65 - 336 * q^66 - 16 * q^67 - 72 * q^68 - 140 * q^69 - 214 * q^70 + 44 * q^71 - 274 * q^72 - 14 * q^73 - 68 * q^74 - 12 * q^75 - 166 * q^76 - 44 * q^77 + 8 * q^78 - 28 * q^79 - 164 * q^80 - 134 * q^81 - 100 * q^82 + 32 * q^83 + 266 * q^84 - 130 * q^86 + 198 * q^87 + 2 * q^88 + 18 * q^89 + 440 * q^90 - 56 * q^91 - 56 * q^92 - 18 * q^93 + 86 * q^94 - 28 * q^95 - 228 * q^96 - 28 * q^97 + 140 * q^98 + 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.u.a	$833$	$2$	833.u	49.g	$21$	$420$	$35$	$6.652$		None		✓			833.2.u.a	$2$	$0$	\(-2\)	\(1\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
833.2.u.b	$833$	$2$	833.u	49.g	$21$	$468$	$39$	$6.652$		None		✓	✓		833.2.u.b	$2$	$0$	\(2\)	\(1\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{21}]$

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

\( S_{2}^{\mathrm{old}}(833, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)