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

• Label: 588.2.ba
• Level: $588$
• Weight: $2$
• Character orbit: 588.ba
• Rep. character: $\chi_{588}(103,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $672$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.ba (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 196 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	1392	672	720
Cusp forms	1296	672	624
Eisenstein series	96	0	96

Trace form

\( 672 q - 12 q^{8} + 56 q^{9} + O(q^{10}) \)

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.ba.a	$588$	$2$	588.ba	196.p	$42$	$336$	$28$	$4.695$		None		$2$	$0$	\(0\)	\(-28\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{42}]$
588.2.ba.b	$588$	$2$	588.ba	196.p	$42$	$336$	$28$	$4.695$		None		$2$	$0$	\(0\)	\(28\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{42}]$

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

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)