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

• Label: 1248.2.q
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.q
• Rep. character: $\chi_{1248}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $14$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(448\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\), \(19\)

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

\( 56 q - 8 q^{5} - 28 q^{9} + O(q^{10}) \)

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.q.a	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(6+\cdots)q^{11}+\cdots\)
1248.2.q.b	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.c	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(8\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+4q^{5}-3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.d	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
1248.2.q.e	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+3q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.f	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(8\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4q^{5}+3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.g	$1248$	$2$	1248.q	13.c	$3$	$4$	$2$	$9.965$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1248.2.q.h	$1248$	$2$	1248.q	13.c	$3$	$4$	$2$	$9.965$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
1248.2.q.i	$1248$	$2$	1248.q	13.c	$3$	$4$	$2$	$9.965$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1248.2.q.j	$1248$	$2$	1248.q	13.c	$3$	$4$	$2$	$9.965$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{3}+\beta _{3}q^{5}+(-\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1248.2.q.k	$1248$	$2$	1248.q	13.c	$3$	$6$	$3$	$9.965$	6.0.7873200.1	None		$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-q^{5}+(\beta _{2}-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1248.2.q.l	$1248$	$2$	1248.q	13.c	$3$	$6$	$3$	$9.965$	6.0.7873200.1	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-q^{5}+(-\beta _{2}+\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1248.2.q.m	$1248$	$2$	1248.q	13.c	$3$	$8$	$4$	$9.965$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(-6\)	\(1\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1248.2.q.n	$1248$	$2$	1248.q	13.c	$3$	$8$	$4$	$9.965$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(-6\)	\(-1\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)