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

• Label: 588.2.y
• Level: $588$
• Weight: $2$
• Character orbit: 588.y
• Rep. character: $\chi_{588}(25,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $108$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.y (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1416	108	1308
Cusp forms	1272	108	1164
Eisenstein series	144	0	144

Trace form

108 * q - q^3 - 2 * q^5 - q^7 + 9 * q^9 - 12 * q^11 + 6 * q^13 + 10 * q^15 - 6 * q^17 + 27 * q^19 + 4 * q^21 + 4 * q^23 + 7 * q^25 + 2 * q^27 + 3 * q^31 - 2 * q^33 + 18 * q^35 - 4 * q^37 + 24 * q^39 + 44 * q^41 - 22 * q^43 + 26 * q^45 + 20 * q^47 + 69 * q^49 + 52 * q^51 + 56 * q^53 + 8 * q^55 - 10 * q^57 + 88 * q^59 + 29 * q^61 + 12 * q^63 + 10 * q^65 + 9 * q^67 + 16 * q^69 + 20 * q^71 - 53 * q^73 + q^75 - 50 * q^77 + q^79 + 9 * q^81 - 158 * q^83 + 56 * q^85 + 10 * q^87 - 154 * q^89 - 81 * q^91 + q^93 - 218 * q^95 + 36 * q^97 - 4 * q^99

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.y.a	$588$	$2$	588.y	49.g	$21$	$48$	$4$	$4.695$		None		✓			588.2.y.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
588.2.y.b	$588$	$2$	588.y	49.g	$21$	$60$	$5$	$4.695$		None		✓	✓		588.2.y.b	$2$	$0$	\(0\)	\(-5\)	\(-2\)	\(-1\)		$\mathrm{SU}(2)[C_{21}]$

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

\( S_{2}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)