Space of modular forms of level 1088, weight 2, and Character 1088.r

• Label: 1088.2.r
• Level: $1088$
• Weight: $2$
• Character orbit: 1088.r
• Rep. character: $\chi_{1088}(305,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 272 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1088, [\chi])\).

	Total	New	Old
Modular forms	304	76	228
Cusp forms	272	68	204
Eisenstein series	32	8	24

Trace form

68 * q - 4 * q^13 + 24 * q^15 - 4 * q^17 - 12 * q^19 - 16 * q^21 - 8 * q^33 + 24 * q^35 + 4 * q^43 - 32 * q^47 + 36 * q^49 - 32 * q^51 - 4 * q^53 - 28 * q^59 + 4 * q^67 - 48 * q^69 - 32 * q^77 - 44 * q^81 + 44 * q^83 - 8 * q^85 + 8 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(1088, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1088.2.r.a	$1088$	$2$	1088.r	272.r	$4$	$68$	$34$	$8.688$		None			✓	✓	272.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1088, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)