Space of modular forms of level 841, weight 2, and Character 841.h

• Label: 841.2.h
• Level: $841$
• Weight: $2$
• Character orbit: 841.h
• Rep. character: $\chi_{841}(28,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $2016$
• Newform subspaces: $1$
• Sturm bound: $145$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.h (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 841 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(145\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(841, [\chi])\).

	Total	New	Old
Modular forms	2072	2072	0
Cusp forms	2016	2016	0
Eisenstein series	56	56	0

Trace form

2016 * q - 29 * q^2 - 29 * q^3 + 47 * q^4 - 23 * q^5 - 39 * q^6 + 25 * q^7 - 29 * q^8 + 45 * q^9 - 29 * q^10 + 29 * q^11 - 29 * q^12 - 27 * q^13 - 29 * q^15 - 97 * q^16 - 116 * q^17 - 29 * q^18 - 29 * q^19 - 47 * q^20 - 29 * q^21 - 13 * q^22 + 17 * q^23 - 25 * q^24 - 107 * q^25 + 29 * q^26 - 29 * q^27 - 127 * q^28 - 23 * q^29 - 5 * q^30 - 29 * q^31 - 29 * q^32 - 33 * q^33 - 43 * q^34 - 104 * q^35 - 111 * q^36 - 29 * q^37 - 23 * q^38 - 29 * q^39 - 29 * q^40 + 363 * q^42 - 29 * q^43 - 29 * q^44 + 127 * q^45 - 261 * q^46 - 174 * q^47 - 29 * q^48 - 267 * q^49 - 29 * q^50 - 5 * q^51 - 41 * q^52 - 15 * q^53 - 45 * q^54 - 29 * q^55 + 87 * q^56 - 25 * q^57 - 9 * q^58 - 101 * q^59 - 29 * q^61 + 3 * q^62 - 336 * q^63 + 369 * q^64 + 104 * q^65 + 87 * q^66 - 43 * q^67 - 29 * q^68 - 87 * q^69 + 116 * q^70 - 25 * q^71 + 406 * q^72 - 29 * q^73 - 263 * q^74 - 29 * q^75 - 348 * q^76 - 29 * q^77 - 31 * q^78 - 29 * q^79 - 25 * q^80 - 81 * q^81 - q^82 + 97 * q^83 + 145 * q^84 - 29 * q^85 - 49 * q^86 - 49 * q^87 - 399 * q^88 - 87 * q^89 - 261 * q^90 - 100 * q^91 + 17 * q^92 - 49 * q^93 - 27 * q^94 - 29 * q^95 + 13 * q^96 - 29 * q^97 + 174 * q^98 - 319 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(841, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
841.2.h.a	$841$	$2$	841.h	841.h	$58$	$2016$	$72$	$6.715$		None		✓	✓	✓	841.2.h.a	$2$	$0$	\(-29\)	\(-29\)	\(-23\)	\(25\)		$\mathrm{SU}(2)[C_{58}]$