Space of modular forms of level 62, weight 2, and Character 62.c

• Label: 62.2.c
• Level: $62$
• Weight: $2$
• Character orbit: 62.c
• Rep. character: $\chi_{62}(5,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(62, [\chi])\).

	Total	New	Old
Modular forms	20	4	16
Cusp forms	12	4	8
Eisenstein series	8	0	8

Trace form

4 * q - 4 * q^3 + 4 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 4 * q^9 - 4 * q^10 - 4 * q^12 - 10 * q^13 + 2 * q^14 + 4 * q^16 - 6 * q^17 - 8 * q^18 + 2 * q^20 + 10 * q^21 + 6 * q^22 - 8 * q^23 - 2 * q^24 + 8 * q^27 + 4 * q^28 + 16 * q^29 + 12 * q^30 - 12 * q^33 - 4 * q^36 + 6 * q^37 - 14 * q^38 + 40 * q^39 - 4 * q^40 + 6 * q^41 + 8 * q^42 - 4 * q^43 - 12 * q^45 - 8 * q^46 - 40 * q^47 - 4 * q^48 + 4 * q^49 + 8 * q^50 - 12 * q^51 - 10 * q^52 - 6 * q^53 + 28 * q^54 + 12 * q^55 + 2 * q^56 - 14 * q^57 - 8 * q^58 - 8 * q^61 + 8 * q^62 - 32 * q^63 + 4 * q^64 + 10 * q^65 - 24 * q^66 + 16 * q^67 - 6 * q^68 + 12 * q^69 - 12 * q^70 + 4 * q^71 - 8 * q^72 + 6 * q^73 - 8 * q^74 + 8 * q^75 + 12 * q^77 + 20 * q^78 + 2 * q^80 - 10 * q^81 + 12 * q^82 + 4 * q^83 + 10 * q^84 - 12 * q^85 + 6 * q^86 - 12 * q^87 + 6 * q^88 + 24 * q^89 - 40 * q^91 - 8 * q^92 + 14 * q^93 + 8 * q^94 + 56 * q^95 - 2 * q^96 + 32 * q^97 - 8 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(62, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
62.2.c.a	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	\(\Q(\sqrt{-3}) \)	None		✓			62.2.c.a	$2$	$0$	\(-2\)	\(-1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
62.2.c.b	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	\(\Q(\sqrt{-3}) \)	None		✓			62.2.c.b	$2$	$0$	\(2\)	\(-3\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(62, [\chi])\) into lower level spaces

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