Space of modular forms of level 84, weight 2, and Character 84.k

• Label: 84.2.k
• Level: $84$
• Weight: $2$
• Character orbit: 84.k
• Rep. character: $\chi_{84}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(84, [\chi])\).

	Total	New	Old
Modular forms	44	6	38
Cusp forms	20	6	14
Eisenstein series	24	0	24

Trace form

6 * q + 3 * q^7 - 18 * q^15 - 9 * q^19 - 9 * q^21 - 3 * q^25 - 9 * q^31 + 27 * q^33 - 3 * q^37 + 9 * q^39 + 42 * q^43 + 27 * q^45 + 15 * q^49 + 9 * q^51 - 36 * q^57 - 54 * q^61 - 15 * q^67 - 45 * q^73 + 27 * q^75 - 15 * q^79 + 36 * q^85 - 9 * q^91 - 54 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(84, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.2.k.a	$84$	$2$	84.k	21.g	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	None		✓			84.2.k.a	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
84.2.k.b	$84$	$2$	84.k	21.g	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	None		✓			84.2.k.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
84.2.k.c	$84$	$2$	84.k	21.g	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			84.2.k.c	$4$	$0$	\(0\)	\(3\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(84, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)