Space of modular forms of level 288, weight 5, and Character 288.b

• Label: 288.5.b
• Level: $288$
• Weight: $5$
• Character orbit: 288.b
• Rep. character: $\chi_{288}(271,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	288.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(288, [\chi])\).

	Total	New	Old
Modular forms	208	21	187
Cusp forms	176	19	157
Eisenstein series	32	2	30

Trace form

19 * q + 94 * q^11 - 118 * q^17 + 706 * q^19 - 2045 * q^25 - 1344 * q^35 - 1462 * q^41 - 1694 * q^43 - 2957 * q^49 + 2782 * q^59 - 576 * q^65 - 3326 * q^67 + 2918 * q^73 - 17282 * q^83 - 982 * q^89 - 28032 * q^91 + 1862 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(288, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.5.b.a	$288$	$5$	288.b	8.d	$2$	$1$	$1$	$29.771$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓				8.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-46q^{11}+574q^{17}-434q^{19}+5^{4}q^{25}+\cdots\)
288.5.b.b	$288$	$5$	288.b	8.d	$2$	$2$	$2$	$29.771$	\(\Q(\sqrt{-15}) \)	None					8.5.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+2\beta q^{7}-26q^{11}-\beta q^{13}+\cdots\)
288.5.b.c	$288$	$5$	288.b	8.d	$2$	$8$	$8$	$29.771$	8.0.\(\cdots\).5	None					72.5.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{4}q^{7}+\beta _{1}q^{11}+(\beta _{4}+\beta _{7})q^{13}+\cdots\)
288.5.b.d	$288$	$5$	288.b	8.d	$2$	$8$	$8$	$29.771$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					24.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(24-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)