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

• Label: 82.2.b
• Level: $82$
• Weight: $2$
• Character orbit: 82.b
• Rep. character: $\chi_{82}(81,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	12	4	8
Cusp forms	8	4	4
Eisenstein series	4	0	4

Trace form

4 * q + 4 * q^4 - 4 * q^5 - 4 * q^10 + 4 * q^16 - 4 * q^18 - 4 * q^20 - 4 * q^21 - 16 * q^23 - 12 * q^25 + 16 * q^31 + 28 * q^33 + 12 * q^37 - 16 * q^39 - 4 * q^40 + 4 * q^41 + 20 * q^42 + 16 * q^43 + 4 * q^45 - 16 * q^46 - 16 * q^49 + 8 * q^50 + 16 * q^51 + 4 * q^57 - 32 * q^59 - 16 * q^62 + 4 * q^64 + 20 * q^66 - 4 * q^72 - 4 * q^73 - 20 * q^74 - 12 * q^77 - 16 * q^78 - 4 * q^80 - 32 * q^81 + 16 * q^82 - 4 * q^84 + 32 * q^86 + 4 * q^90 + 16 * q^91 - 16 * q^92 + 28 * q^98

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.b.a	$82$	$2$	82.b	41.b	$2$	$2$	$2$	$0.655$	\(\Q(\sqrt{-2}) \)	None		✓			82.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+3\beta q^{7}+\cdots\)
82.2.b.b	$82$	$2$	82.b	41.b	$2$	$2$	$2$	$0.655$	\(\Q(\sqrt{-1}) \)	None		✓			82.2.b.b	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta q^{3}+q^{4}-2 q^{5}+\beta q^{6}+\cdots\)

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

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