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 + 18 * q^10 + 22 * q^14 + 8 * q^16 + 8 * q^21 + 12 * q^22 + 24 * q^24 - 52 * q^25 - 30 * q^26 + 36 * q^28 - 8 * q^30 - 10 * q^32 + 12 * q^33 + 112 * q^34 + 32 * q^37 - 18 * q^38 - 26 * q^40 - 16 * q^42 - 64 * q^44 - 8 * q^49 - 228 * q^50 - 36 * q^52 - 8 * q^53 - 40 * q^56 - 24 * q^57 - 6 * q^58 + 10 * q^60 + 4 * q^61 - 8 * q^65 + 36 * q^66 + 36 * q^68 - 108 * q^70 + 48 * q^72 + 36 * q^73 + 22 * q^74 + 42 * q^76 - 16 * q^77 - 12 * q^78 - 54 * q^80 + 56 * q^81 - 186 * q^82 + 40 * q^84 + 48 * q^85 - 188 * q^86 - 284 * q^88 + 28 * q^92 - 4 * q^93 - 336 * q^94 - 30 * q^96 - 278 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓			588.2.ba.a	$2$	$0$	\(0\)	\(-28\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{42}]$
588.2.ba.b	$588$	$2$	588.ba	196.p	$42$	$336$	$28$	$4.695$		None		✓			588.2.ba.a	$2$	$0$	\(0\)	\(28\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{42}]$

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

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