Space of modular forms of level 1014, weight 3, and Character 1014.f

• Label: 1014.3.f
• Level: $1014$
• Weight: $3$
• Character orbit: 1014.f
• Rep. character: $\chi_{1014}(577,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $12$
• Sturm bound: $546$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(546\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1014, [\chi])\).

	Total	New	Old
Modular forms	784	100	684
Cusp forms	672	100	572
Eisenstein series	112	0	112

Trace form

\( 100 q + 4 q^{2} - 12 q^{5} - 8 q^{8} + 300 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1014, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1014.3.f.a	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-4\)	\(0\)	\(-12\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}-2\zeta_{12}q^{4}+\cdots\)
1014.3.f.b	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-4\)	\(0\)	\(6\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
1014.3.f.c	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-4\)	\(0\)	\(8\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\zeta_{12})q^{2}-\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\)
1014.3.f.d	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-4\)	\(0\)	\(12\)	\(10\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
1014.3.f.e	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(4\)	\(0\)	\(-12\)	\(-10\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
1014.3.f.f	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(4\)	\(0\)	\(-8\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{12})q^{2}-\zeta_{12}^{3}q^{3}-2\zeta_{12}q^{4}+\cdots\)
1014.3.f.g	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(4\)	\(0\)	\(-6\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
1014.3.f.h	$1014$	$3$	1014.f	13.d	$4$	$8$	$4$	$27.629$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-8\)	\(0\)	\(-6\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+(-\beta _{3}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
1014.3.f.i	$1014$	$3$	1014.f	13.d	$4$	$8$	$4$	$27.629$	8.0.\(\cdots\).1	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{6})q^{2}+\beta _{1}q^{3}-2\beta _{6}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1014.3.f.j	$1014$	$3$	1014.f	13.d	$4$	$8$	$4$	$27.629$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(8\)	\(0\)	\(6\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+(-\beta _{3}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
1014.3.f.k	$1014$	$3$	1014.f	13.d	$4$	$24$	$12$	$27.629$		None		$2$	$0$	\(-24\)	\(0\)	\(-8\)	\(-24\)		$\mathrm{SU}(2)[C_{4}]$
1014.3.f.l	$1014$	$3$	1014.f	13.d	$4$	$24$	$12$	$27.629$		None		$2$	$0$	\(24\)	\(0\)	\(8\)	\(24\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)