Space of modular forms of level 288, weight 8, and Character 288.d

• Label: 288.8.d
• Level: $288$
• Weight: $8$
• Character orbit: 288.d
• Rep. character: $\chi_{288}(145,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	288.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(288, [\chi])\).

	Total	New	Old
Modular forms	352	36	316
Cusp forms	320	34	286
Eisenstein series	32	2	30

Trace form

\( 34 q + 688 q^{7} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(288, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.8.d.a	$288$	$8$	288.d	8.b	$2$	$2$	$2$	$89.967$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1508\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+197\beta q^{5}+754q^{7}-2378\beta q^{11}+\cdots\)
288.8.d.b	$288$	$8$	288.d	8.b	$2$	$6$	$6$	$89.967$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(688\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{3})q^{5}+(115+\beta _{1})q^{7}+(3\beta _{2}+\cdots)q^{11}+\cdots\)
288.8.d.c	$288$	$8$	288.d	8.b	$2$	$12$	$12$	$89.967$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-136\)	$2^{72}\cdot 3^{6}\cdot 5^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-11+\beta _{4})q^{7}+(-10\beta _{1}+\cdots)q^{11}+\cdots\)
288.8.d.d	$288$	$8$	288.d	8.b	$2$	$14$	$14$	$89.967$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1372\)	$2^{88}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(-98+\beta _{3})q^{7}+(-4\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(288, [\chi]) \cong \)