Space of modular forms of level 82, weight 2, and Character 82.g

• Label: 82.2.g
• Level: $82$
• Weight: $2$
• Character orbit: 82.g
• Rep. character: $\chi_{82}(5,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	82.g (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(21\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(82, [\chi])\).

	Total	New	Old
Modular forms	104	24	80
Cusp forms	72	24	48
Eisenstein series	32	0	32

Trace form

24 * q - 2 * q^3 + 6 * q^4 - 4 * q^6 + 4 * q^10 + 10 * q^11 + 2 * q^12 - 16 * q^13 - 20 * q^14 - 44 * q^15 - 6 * q^16 - 10 * q^17 + 6 * q^18 - 20 * q^19 - 14 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^25 + 16 * q^27 - 16 * q^29 + 8 * q^30 + 36 * q^31 - 40 * q^33 + 2 * q^34 + 64 * q^35 + 10 * q^36 + 8 * q^37 + 18 * q^38 + 80 * q^39 + 16 * q^40 - 16 * q^41 + 16 * q^42 - 20 * q^43 + 10 * q^44 + 52 * q^45 + 20 * q^46 + 24 * q^47 + 8 * q^48 + 40 * q^49 + 16 * q^51 - 4 * q^52 + 28 * q^53 + 20 * q^54 - 52 * q^55 - 52 * q^57 + 4 * q^58 - 12 * q^59 - 56 * q^60 - 80 * q^61 - 48 * q^63 + 6 * q^64 - 32 * q^65 - 12 * q^66 + 44 * q^67 + 16 * q^69 - 36 * q^70 - 40 * q^71 - 6 * q^72 + 8 * q^75 - 10 * q^76 - 20 * q^77 - 52 * q^78 - 56 * q^79 + 60 * q^81 + 10 * q^82 - 44 * q^83 + 60 * q^85 - 28 * q^86 - 40 * q^87 - 26 * q^88 + 10 * q^89 - 8 * q^92 - 48 * q^93 + 16 * q^94 - 44 * q^95 + 6 * q^96 - 26 * q^97 - 22 * q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(82, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
82.2.g.a	$82$	$2$	82.g	41.g	$20$	$8$	$1$	$0.655$	\(\Q(\zeta_{20})\)	None		✓			82.2.g.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q-\zeta_{20}^{3}q^{2}+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)
82.2.g.b	$82$	$2$	82.g	41.g	$20$	$16$	$2$	$0.655$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		82.2.g.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q-\beta _{12}q^{2}+(-2+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(82, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(82, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)