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

• Label: 82.2.c
• Level: $82$
• Weight: $2$
• Character orbit: 82.c
• Rep. character: $\chi_{82}(9,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $21$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	82.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(21\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	26	6	20
Cusp forms	18	6	12
Eisenstein series	8	0	8

Trace form

\( 6 q + 2 q^{3} - 6 q^{4} - 6 q^{6} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
82.2.c.a	$82$	$2$	82.c	41.c	$4$	$2$	$1$	$0.655$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}+(-1+i)q^{3}-q^{4}+2iq^{5}+\cdots\)
82.2.c.b	$82$	$2$	82.c	41.c	$4$	$2$	$1$	$0.655$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}-q^{4}-2iq^{5}+(3-3i)q^{7}+\cdots\)
82.2.c.c	$82$	$2$	82.c	41.c	$4$	$2$	$1$	$0.655$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}+(2-2i)q^{3}-q^{4}+2iq^{5}+\cdots\)

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

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