Space of modular forms of level 1264, weight 2, and Character 1264.n

• Label: 1264.2.n
• Level: $1264$
• Weight: $2$
• Character orbit: 1264.n
• Rep. character: $\chi_{1264}(735,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $9$
• Sturm bound: $320$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 316 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(320\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1264, [\chi])\).

	Total	New	Old
Modular forms	332	80	252
Cusp forms	308	80	228
Eisenstein series	24	0	24

Trace form

\( 80 q - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1264, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1264.2.n.a	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	\(\Q(\sqrt{-3}) \)	None		✓	1264.2.n.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1264.2.n.b	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	\(\Q(\sqrt{-3}) \)	None		✓	1264.2.n.b	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1264.2.n.c	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	\(\Q(\sqrt{-3}) \)	None		✓	1264.2.n.c	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+\zeta_{6}q^{7}+\cdots\)
1264.2.n.d	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	\(\Q(\sqrt{-3}) \)	None		✓	1264.2.n.c	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1264.2.n.e	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	\(\Q(\sqrt{-3}) \)	None		✓	1264.2.n.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-4+\cdots)q^{13}+\cdots\)
1264.2.n.f	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	\(\Q(\sqrt{-3}) \)	None		✓	1264.2.n.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
1264.2.n.g	$1264$	$2$	1264.n	316.f	$6$	$20$	$10$	$10.093$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	1264.2.n.g	$2$	$0$	\(0\)	\(-4\)	\(3\)	\(-8\)	$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{3}+(-\beta _{11}-\beta _{14})q^{5}+(\beta _{8}-\beta _{19})q^{7}+\cdots\)
1264.2.n.h	$1264$	$2$	1264.n	316.f	$6$	$20$	$10$	$10.093$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	1264.2.n.g	$2$	$0$	\(0\)	\(4\)	\(3\)	\(8\)	$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{3}+(-\beta _{11}-\beta _{14})q^{5}+(-\beta _{8}+\cdots)q^{7}+\cdots\)
1264.2.n.i	$1264$	$2$	1264.n	316.f	$6$	$28$	$14$	$10.093$		None		✓	1264.2.n.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1264, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1264, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(316, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(632, [\chi])\)\(^{\oplus 2}\)