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

• Label: 1248.2.g
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.g
• Rep. character: $\chi_{1248}(625,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	240	24	216
Cusp forms	208	24	184
Eisenstein series	32	0	32

Trace form

\( 24 q - 8 q^{7} - 24 q^{9} + 8 q^{15} + 16 q^{23} - 24 q^{25} + 8 q^{31} - 8 q^{39} - 48 q^{47} + 24 q^{49} + 16 q^{55} + 8 q^{63} - 16 q^{71} + 24 q^{81} + 48 q^{95} - 16 q^{97}+O(q^{100}) \)

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.g.a	$1248$	$2$	1248.g	8.b	$2$	$8$	$8$	$9.965$	\(\Q(\zeta_{20})\)	None					312.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{3}+(\beta_{2}-\beta_1)q^{5}+(-\beta_{5}-1)q^{7}+\cdots\)
1248.2.g.b	$1248$	$2$	1248.g	8.b	$2$	$16$	$16$	$9.965$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		312.2.g.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{12}q^{5}-\beta _{5}q^{7}-q^{9}+\beta _{10}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)