Space of modular forms of level 84, weight 3, and Character 84.h

• Label: 84.3.h
• Level: $84$
• Weight: $3$
• Character orbit: 84.h
• Rep. character: $\chi_{84}(83,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	84.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(84, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

28 * q - 4 * q^4 - 4 * q^9 + 4 * q^16 - 44 * q^18 - 28 * q^21 - 48 * q^22 + 68 * q^25 + 68 * q^28 - 68 * q^30 - 64 * q^36 - 88 * q^37 + 92 * q^42 - 8 * q^46 - 68 * q^49 - 24 * q^57 + 280 * q^58 + 28 * q^60 + 188 * q^64 - 248 * q^70 + 484 * q^72 + 372 * q^78 - 4 * q^81 - 284 * q^84 - 192 * q^85 - 112 * q^88 + 120 * q^93

Decomposition of \(S_{3}^{\mathrm{new}}(84, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.3.h.a	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	\(\Q\)	\(\Q(\sqrt{-21}) \)	✓	✓			84.3.h.a	$2$	$0$	\(-2\)	\(-3\)	\(-4\)	\(7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-3q^{3}+4q^{4}-4q^{5}+6q^{6}+\cdots\)
84.3.h.b	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	\(\Q\)	\(\Q(\sqrt{-21}) \)	✓	✓			84.3.h.a	$2$	$0$	\(-2\)	\(3\)	\(4\)	\(-7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+3q^{3}+4q^{4}+4q^{5}-6q^{6}+\cdots\)
84.3.h.c	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	\(\Q\)	\(\Q(\sqrt{-21}) \)	✓	✓			84.3.h.a	$2$	$0$	\(2\)	\(-3\)	\(4\)	\(7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-3q^{3}+4q^{4}+4q^{5}-6q^{6}+\cdots\)
84.3.h.d	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	\(\Q\)	\(\Q(\sqrt{-21}) \)	✓	✓			84.3.h.a	$2$	$0$	\(2\)	\(3\)	\(-4\)	\(-7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+3q^{3}+4q^{4}-4q^{5}+6q^{6}+\cdots\)
84.3.h.e	$84$	$3$	84.h	84.h	$2$	$24$	$24$	$2.289$		None		✓	✓		84.3.h.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$