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

• Label: 62.2.d
• Level: $62$
• Weight: $2$
• Character orbit: 62.d
• Rep. character: $\chi_{62}(33,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
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	40	16	24
Cusp forms	24	16	8
Eisenstein series	16	0	16

Trace form

16 * q - 6 * q^3 - 4 * q^4 - 4 * q^5 + 8 * q^6 - 2 * q^7 - 12 * q^9 - 4 * q^10 + 4 * q^11 - 6 * q^12 - 4 * q^13 + 6 * q^14 - 2 * q^15 - 4 * q^16 - 2 * q^17 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 6 * q^21 - 8 * q^22 - 12 * q^23 - 2 * q^24 + 16 * q^25 + 32 * q^26 + 42 * q^27 + 8 * q^28 - 6 * q^29 - 16 * q^30 + 28 * q^31 + 32 * q^33 + 8 * q^34 - 28 * q^35 + 28 * q^36 + 12 * q^37 + 18 * q^38 + 14 * q^39 + 6 * q^40 - 18 * q^41 - 18 * q^42 - 10 * q^43 - 6 * q^44 - 50 * q^45 - 12 * q^46 - 22 * q^47 + 4 * q^48 - 4 * q^49 + 4 * q^50 + 6 * q^51 - 4 * q^52 + 16 * q^53 - 32 * q^54 - 20 * q^55 - 4 * q^56 + 8 * q^57 - 18 * q^58 + 4 * q^59 - 2 * q^60 + 16 * q^61 + 2 * q^62 + 72 * q^63 - 4 * q^64 - 16 * q^65 - 8 * q^66 - 52 * q^67 + 8 * q^68 - 46 * q^69 - 28 * q^70 - 40 * q^71 - 8 * q^72 + 6 * q^73 - 28 * q^74 - 8 * q^75 + 24 * q^76 + 26 * q^77 + 14 * q^78 + 4 * q^79 + 6 * q^80 - 2 * q^81 - 4 * q^82 + 62 * q^83 - 16 * q^84 + 24 * q^85 + 26 * q^86 - 12 * q^87 + 32 * q^88 - 6 * q^89 + 42 * q^90 + 22 * q^91 - 32 * q^92 + 24 * q^93 - 8 * q^94 + 18 * q^95 - 2 * q^96 + 16 * q^97 + 104 * q^98 - 32 * 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.d.a	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.511890625.1	None		✓			62.2.d.a	$2$	$0$	\(-2\)	\(-4\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
62.2.d.b	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.1903140625.1	None		✓			62.2.d.b	$2$	$0$	\(2\)	\(-2\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{6}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

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

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