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

• Label: 1248.2.bb
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.bb
• Rep. character: $\chi_{1248}(463,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $6$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
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	480	56	424
Cusp forms	416	56	360
Eisenstein series	64	0	64

Trace form

\( 56 q + 56 q^{9} - 8 q^{41} - 16 q^{57} + 64 q^{59} + 8 q^{65} - 24 q^{73} + 56 q^{81} + 80 q^{83} + 40 q^{89} + 16 q^{91} + 8 q^{97}+O(q^{100}) \)

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.bb.a	$1248$	$2$	1248.bb	104.m	$4$	$2$	$1$	$9.965$	\(\Q(\sqrt{-1}) \)	None					312.2.t.b	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{3}+(2 i-2)q^{5}+(3 i+3)q^{7}+\cdots\)
1248.2.bb.b	$1248$	$2$	1248.bb	104.m	$4$	$2$	$1$	$9.965$	\(\Q(\sqrt{-1}) \)	None					312.2.t.b	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{3}+(-2 i+2)q^{5}+(-3 i-3)q^{7}+\cdots\)
1248.2.bb.c	$1248$	$2$	1248.bb	104.m	$4$	$2$	$1$	$9.965$	\(\Q(\sqrt{-1}) \)	None					312.2.t.a	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{3}+(2 i-2)q^{5}+(-i-1)q^{7}+\cdots\)
1248.2.bb.d	$1248$	$2$	1248.bb	104.m	$4$	$2$	$1$	$9.965$	\(\Q(\sqrt{-1}) \)	None					312.2.t.a	$2$	$0$	\(0\)	\(2\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{3}+(-2 i+2)q^{5}+(i+1)q^{7}+\cdots\)
1248.2.bb.e	$1248$	$2$	1248.bb	104.m	$4$	$24$	$12$	$9.965$		None					312.2.t.f	$4$	$0$	\(0\)	\(-24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1248.2.bb.f	$1248$	$2$	1248.bb	104.m	$4$	$24$	$12$	$9.965$		None					312.2.t.e	$4$	$0$	\(0\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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