Space of modular forms of level 1098, weight 2, and Character 1098.f

• Label: 1098.2.f
• Level: $1098$
• Weight: $2$
• Character orbit: 1098.f
• Rep. character: $\chi_{1098}(379,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $54$
• Newform subspaces: $9$
• Sturm bound: $372$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1098.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 61 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(372\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1098, [\chi])\).

	Total	New	Old
Modular forms	388	54	334
Cusp forms	356	54	302
Eisenstein series	32	0	32

Trace form

\( 54 q - q^{2} - 27 q^{4} + 5 q^{5} + 4 q^{7} + 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1098, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1098.2.f.a	$1098$	$2$	1098.f	61.c	$3$	$2$	$1$	$8.768$	\(\Q(\sqrt{-3}) \)	None					366.2.e.b	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1098.2.f.b	$1098$	$2$	1098.f	61.c	$3$	$2$	$1$	$8.768$	\(\Q(\sqrt{-3}) \)	None					366.2.e.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
1098.2.f.c	$1098$	$2$	1098.f	61.c	$3$	$4$	$2$	$8.768$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None					122.2.c.a	$2$	$0$	\(-2\)	\(0\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+(3+\cdots)q^{7}+\cdots\)
1098.2.f.d	$1098$	$2$	1098.f	61.c	$3$	$4$	$2$	$8.768$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None					366.2.e.c	$2$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1098.2.f.e	$1098$	$2$	1098.f	61.c	$3$	$6$	$3$	$8.768$	6.0.954288.1	None					366.2.e.e	$2$	$0$	\(-3\)	\(0\)	\(1\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{3}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1098.2.f.f	$1098$	$2$	1098.f	61.c	$3$	$6$	$3$	$8.768$	6.0.65370672.1	None					366.2.e.d	$2$	$0$	\(-3\)	\(0\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-1-\beta _{4})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
1098.2.f.g	$1098$	$2$	1098.f	61.c	$3$	$6$	$3$	$8.768$	6.0.5938947.1	None					122.2.c.b	$2$	$0$	\(3\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{2}-\beta _{4}q^{4}+(-1+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1098.2.f.h	$1098$	$2$	1098.f	61.c	$3$	$12$	$6$	$8.768$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1098.2.f.h	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}+\beta _{4}q^{7}+\cdots\)
1098.2.f.i	$1098$	$2$	1098.f	61.c	$3$	$12$	$6$	$8.768$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1098.2.f.h	$2$	$0$	\(6\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}-\beta _{5}q^{5}+\beta _{4}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1098, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1098, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(122, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(183, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(366, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(549, [\chi])\)\(^{\oplus 2}\)