Space of modular forms of level 1248, weight 2, and Character 1248.n

• Label: 1248.2.n
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.n
• Rep. character: $\chi_{1248}(1247,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $5$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(448\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

	Total	New	Old
Modular forms	240	56	184
Cusp forms	208	56	152
Eisenstein series	32	0	32

Trace form

\( 56 q + 8 q^{13} + 56 q^{25} + 72 q^{49} - 48 q^{61} + 32 q^{69} + 32 q^{81}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1248.2.n.a	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	\(\Q(\zeta_{8})\)	None		✓			1248.2.n.a	$2$	$0$	\(0\)	\(-4\)	\(-8\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}-1)q^{3}+(\beta_{3}-2)q^{5}+(-\beta_{3}+2)q^{7}+\cdots\)
1248.2.n.b	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	\(\Q(\zeta_{8})\)	None		✓			1248.2.n.a	$2$	$0$	\(0\)	\(-4\)	\(8\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}-1)q^{3}+(\beta_{3}+2)q^{5}+(-\beta_{3}-2)q^{7}+\cdots\)
1248.2.n.c	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	\(\Q(\zeta_{8})\)	None		✓			1248.2.n.a	$2$	$0$	\(0\)	\(4\)	\(-8\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+1)q^{3}+(\beta_{3}-2)q^{5}+(\beta_{3}-2)q^{7}+\cdots\)
1248.2.n.d	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	\(\Q(\zeta_{8})\)	None		✓			1248.2.n.a	$2$	$0$	\(0\)	\(4\)	\(8\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+1)q^{3}+(-\beta_{3}+2)q^{5}+\cdots\)
1248.2.n.e	$1248$	$2$	1248.n	156.h	$2$	$40$	$40$	$9.965$		None		✓	✓		1248.2.n.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)