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

• Label: 1248.2.c
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.c
• Rep. character: $\chi_{1248}(961,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $448$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(448\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	240	28	212
Cusp forms	208	28	180
Eisenstein series	32	0	32

Trace form

\( 28 q + 28 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1248.2.c.a	$1248$	$2$	1248.c	13.b	$2$	$6$	$6$	$9.965$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
1248.2.c.b	$1248$	$2$	1248.c	13.b	$2$	$6$	$6$	$9.965$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1248.2.c.c	$1248$	$2$	1248.c	13.b	$2$	$8$	$8$	$9.965$	8.0.134560000.4	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1248.2.c.d	$1248$	$2$	1248.c	13.b	$2$	$8$	$8$	$9.965$	8.0.134560000.4	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)