Space of modular forms of level 62, weight 2, and trivial character

• Label: 62.2.a
• Level: $62$
• Weight: $2$
• Character orbit: 62.a
• Rep. character: $\chi_{62}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(62))\).

	Total	New	Old
Modular forms	10	3	7
Cusp forms	7	3	4
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(31\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(3\)

Trace form

3 * q - q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 - q^8 - q^9 - 2 * q^10 - 6 * q^11 + 2 * q^12 - 4 * q^14 - 12 * q^15 + 3 * q^16 - 6 * q^17 - 5 * q^18 - 4 * q^19 - 2 * q^20 + 4 * q^21 + 6 * q^22 + 8 * q^23 - 2 * q^24 + 13 * q^25 + 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^29 + 12 * q^30 + q^31 - q^32 - 6 * q^34 - q^36 + 20 * q^37 + 12 * q^38 - 20 * q^39 - 2 * q^40 + 6 * q^41 - 4 * q^42 + 6 * q^43 - 6 * q^44 - 18 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 - 13 * q^49 - 15 * q^50 + 12 * q^51 - 8 * q^54 - 12 * q^55 - 4 * q^56 - 8 * q^57 + 8 * q^58 - 24 * q^59 - 12 * q^60 - 8 * q^61 - 3 * q^62 + 4 * q^63 + 3 * q^64 + 32 * q^65 + 4 * q^67 - 6 * q^68 + 8 * q^71 - 5 * q^72 - 10 * q^73 + 14 * q^75 - 4 * q^76 - 12 * q^77 + 20 * q^78 - 4 * q^79 - 2 * q^80 + 11 * q^81 - 18 * q^82 + 14 * q^83 + 4 * q^84 - 12 * q^85 + 10 * q^86 + 12 * q^87 + 6 * q^88 + 6 * q^89 + 30 * q^90 - 4 * q^91 + 8 * q^92 + 2 * q^93 - 20 * q^94 - 8 * q^95 - 2 * q^96 + 6 * q^97 - q^98 + 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(62))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	31
62.2.a.a	$62$	$2$	62.a	1.a	$1$	$1$	$1$	$0.495$	\(\Q\)	None	✓	✓	✓	✓	62.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
62.2.a.b	$62$	$2$	62.a	1.a	$1$	$2$	$2$	$0.495$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	62.2.a.b	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(62))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(62)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)