Space of modular forms of level 59, weight 3, and Character 59.b

• Label: 59.3.b
• Level: $59$
• Weight: $3$
• Character orbit: 59.b
• Rep. character: $\chi_{59}(58,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $2$
• Sturm bound: $15$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	59.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(15\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(59, [\chi])\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	9	9	0
Eisenstein series	2	2	0

Trace form

\( 9 q + 4 q^{3} - 18 q^{4} - 8 q^{5} + 6 q^{7} + 41 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(59, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.3.b.a	$59$	$3$	59.b	59.b	$2$	$3$	$3$	$1.608$	3.3.1593.1	\(\Q(\sqrt{-59}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
59.3.b.b	$59$	$3$	59.b	59.b	$2$	$6$	$6$	$1.608$	6.0.7196038400.1	None		$2$	$0$	\(0\)	\(4\)	\(-8\)	\(6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-5-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)