Space of modular forms of level 62, weight 3, and Character 62.b

• Label: 62.3.b
• Level: $62$
• Weight: $3$
• Character orbit: 62.b
• Rep. character: $\chi_{62}(61,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	62.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(62, [\chi])\).

	Total	New	Old
Modular forms	18	4	14
Cusp forms	14	4	10
Eisenstein series	4	0	4

Trace form

4 * q + 8 * q^4 - 12 * q^5 - 12 * q^7 - 20 * q^9 + 16 * q^10 + 8 * q^14 + 16 * q^16 + 16 * q^18 + 36 * q^19 - 24 * q^20 - 32 * q^25 - 24 * q^28 + 92 * q^31 - 144 * q^33 + 52 * q^35 - 40 * q^36 - 120 * q^38 + 152 * q^39 + 32 * q^40 + 44 * q^41 + 92 * q^45 - 56 * q^47 - 152 * q^49 - 96 * q^50 + 8 * q^51 + 16 * q^56 + 140 * q^59 - 8 * q^62 + 76 * q^63 + 32 * q^64 + 256 * q^66 - 176 * q^67 + 8 * q^69 - 72 * q^70 + 28 * q^71 + 32 * q^72 + 72 * q^76 + 64 * q^78 - 48 * q^80 - 372 * q^81 - 32 * q^82 - 152 * q^87 - 128 * q^90 - 8 * q^93 + 304 * q^94 - 348 * q^95 - 172 * q^97 - 48 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(62, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
62.3.b.a	$62$	$3$	62.b	31.b	$2$	$4$	$4$	$1.689$	4.0.48128.1	None		✓	✓	✓	62.3.b.a	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{2}q^{3}+2q^{4}+(-3+2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(62, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(62, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)