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

• Label: 1248.2.ca
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.ca
• Rep. character: $\chi_{1248}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• 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.ca (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{6})\)
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	480	56	424
Cusp forms	416	56	360
Eisenstein series	64	0	64

Trace form

\( 56 q + 28 q^{9} + 4 q^{17} + 48 q^{25} + 12 q^{41} + 20 q^{49} + 48 q^{55} + 12 q^{65} + 80 q^{79} - 28 q^{81} + 24 q^{87} + 40 q^{95} + 24 q^{97}+O(q^{100}) \)

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.ca.a	$1248$	$2$	1248.ca	104.s	$6$	$8$	$4$	$9.965$	8.0.12960000.1	None					312.2.bk.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1248.2.ca.b	$1248$	$2$	1248.ca	104.s	$6$	$48$	$24$	$9.965$		None			✓		312.2.bk.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{6}]$

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

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