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

• Label: 588.2.i
• Level: $588$
• Weight: $2$
• Character orbit: 588.i
• Rep. character: $\chi_{588}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $7$
• Sturm bound: $224$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(224\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	272	14	258
Cusp forms	176	14	162
Eisenstein series	96	0	96

Trace form

14 * q - q^3 - 2 * q^5 - 7 * q^9 + 2 * q^11 + 6 * q^13 - 4 * q^15 + 8 * q^17 - q^19 + 12 * q^23 - 9 * q^25 + 2 * q^27 - 16 * q^29 + 3 * q^31 - 2 * q^33 - 19 * q^37 - 11 * q^39 - 12 * q^41 + 6 * q^43 - 2 * q^45 + 6 * q^47 - 12 * q^51 + 32 * q^53 + 8 * q^55 + 34 * q^57 + 4 * q^59 - 6 * q^61 + 58 * q^65 + 3 * q^67 + 16 * q^69 + 20 * q^71 - 11 * q^73 + q^75 - 21 * q^79 - 7 * q^81 - 4 * q^83 - 48 * q^85 - 4 * q^87 - 21 * q^93 - 2 * q^95 - 20 * 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.i.a	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None		✓			588.2.a.b	$2$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.b	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None					84.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.c	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None					84.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.d	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None					84.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.e	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None					84.2.a.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.i.f	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None					84.2.a.b	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.g	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	\(\Q(\sqrt{-3}) \)	None		✓			588.2.a.b	$2$	$0$	\(0\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)