Space of modular forms of level 588, weight 2, and Character 588.o

• Label: 588.2.o
• Level: $588$
• Weight: $2$
• Character orbit: 588.o
• Rep. character: $\chi_{588}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $224$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(224\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).

	Total	New	Old
Modular forms	256	80	176
Cusp forms	192	80	112
Eisenstein series	64	0	64

Trace form

\( 80 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
588.2.o.a	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.432972864.2	None		$4$	$0$	\(1\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.b	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.562828176.1	None		$2$	$0$	\(1\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.o.c	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.432972864.2	None		$4$	$0$	\(1\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.d	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.562828176.1	None		$2$	$0$	\(1\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots\)
588.2.o.e	$588$	$2$	588.o	28.f	$6$	$24$	$12$	$4.695$		None		$4$	$0$	\(-4\)	\(-12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
588.2.o.f	$588$	$2$	588.o	28.f	$6$	$24$	$12$	$4.695$		None		$4$	$0$	\(-4\)	\(12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)