Space of modular forms of level 59, weight 2, and trivial character

• Label: 59.2.a
• Level: $59$
• Weight: $2$
• Character orbit: 59.a
• Rep. character: $\chi_{59}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	59.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(59))\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	5	5	0
Eisenstein series	1	1	0

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

\(59\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(-\)		\(6\)	\(6\)	\(0\)		\(5\)	\(5\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

5 * q - 2 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 + 5 * q^9 - 8 * q^10 - 2 * q^11 - 22 * q^12 + 8 * q^13 - 18 * q^14 - 9 * q^15 + 10 * q^16 - q^17 - 2 * q^18 + 6 * q^19 + 6 * q^20 + 15 * q^21 + 8 * q^22 - 8 * q^23 + 6 * q^24 + 7 * q^25 + 8 * q^26 - 11 * q^27 - 2 * q^28 + 14 * q^29 + 14 * q^30 - 2 * q^32 - 14 * q^33 - 2 * q^34 - 9 * q^35 + 42 * q^36 + 18 * q^37 - 18 * q^39 - 18 * q^40 - 10 * q^41 + 34 * q^42 - 4 * q^43 + 12 * q^44 + q^45 + 16 * q^46 - 20 * q^47 - 54 * q^48 + q^49 + 8 * q^50 - 12 * q^51 + 28 * q^52 - 10 * q^53 - 26 * q^54 - 20 * q^55 - 38 * q^56 - 3 * q^57 - 38 * q^58 + 5 * q^59 - 28 * q^60 + 22 * q^61 + 48 * q^62 - 12 * q^63 + 18 * q^64 - 16 * q^65 + 28 * q^66 - 14 * q^68 - 4 * q^69 - 24 * q^70 + 3 * q^71 + 28 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^75 + 14 * q^76 + 2 * q^77 + 20 * q^78 + 10 * q^79 + 50 * q^80 - 3 * q^81 - 48 * q^82 + 6 * q^83 + 28 * q^84 + 40 * q^85 - 8 * q^86 + 11 * q^87 - 24 * q^88 + 10 * q^89 - 8 * q^90 + 6 * q^91 + 4 * q^92 + 6 * q^93 - 36 * q^94 + 26 * q^95 + 42 * q^96 - 22 * q^97 + 24 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		59
59.2.a.a	$59$	$2$	59.a	1.a	$1$	$5$	$5$	$0.471$	5.5.138136.1	None	✓	✓	✓	✓	59.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots\)