Space of modular forms of level 1071, weight 2, and Character 1071.i

• Label: 1071.2.i
• Level: $1071$
• Weight: $2$
• Character orbit: 1071.i
• Rep. character: $\chi_{1071}(613,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $108$
• Newform subspaces: $11$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1071, [\chi])\).

	Total	New	Old
Modular forms	304	108	196
Cusp forms	272	108	164
Eisenstein series	32	0	32

Trace form

\( 108 q - 2 q^{2} - 58 q^{4} + 4 q^{5} + 10 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1071, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1071.2.i.a	$1071$	$2$	1071.i	7.c	$3$	$2$	$1$	$8.552$	\(\Q(\sqrt{-3}) \)	None					357.2.i.c	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1071.2.i.b	$1071$	$2$	1071.i	7.c	$3$	$2$	$1$	$8.552$	\(\Q(\sqrt{-3}) \)	None					357.2.i.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1071.2.i.c	$1071$	$2$	1071.i	7.c	$3$	$2$	$1$	$8.552$	\(\Q(\sqrt{-3}) \)	None					357.2.i.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1071.2.i.d	$1071$	$2$	1071.i	7.c	$3$	$6$	$3$	$8.552$	6.0.64827.1	None					119.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1071.2.i.e	$1071$	$2$	1071.i	7.c	$3$	$8$	$4$	$8.552$	8.0.7007196681.1	None					357.2.i.e	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1071.2.i.f	$1071$	$2$	1071.i	7.c	$3$	$8$	$4$	$8.552$	8.0.1767277521.3	None					357.2.i.d	$2$	$0$	\(-1\)	\(0\)	\(4\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}-\beta _{7})q^{2}+(\beta _{4}+\beta _{5}-2\beta _{6}+\cdots)q^{4}+\cdots\)
1071.2.i.g	$1071$	$2$	1071.i	7.c	$3$	$10$	$5$	$8.552$	10.0.\(\cdots\).1	None					357.2.i.f	$2$	$0$	\(-2\)	\(0\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{6})q^{2}+(-2+\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots\)
1071.2.i.h	$1071$	$2$	1071.i	7.c	$3$	$12$	$6$	$8.552$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					357.2.i.g	$2$	$0$	\(2\)	\(0\)	\(-7\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
1071.2.i.i	$1071$	$2$	1071.i	7.c	$3$	$14$	$7$	$8.552$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					119.2.e.b	$2$	$0$	\(3\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
1071.2.i.j	$1071$	$2$	1071.i	7.c	$3$	$22$	$11$	$8.552$		None		✓			1071.2.i.j	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{3}]$
1071.2.i.k	$1071$	$2$	1071.i	7.c	$3$	$22$	$11$	$8.552$		None		✓			1071.2.i.j	$2$	$0$	\(4\)	\(0\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1071, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1071, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)