Space of modular forms of level 819, weight 2, and Character 819.j

• Label: 819.2.j
• Level: $819$
• Weight: $2$
• Character orbit: 819.j
• Rep. character: $\chi_{819}(235,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $10$
• Sturm bound: $224$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(224\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

	Total	New	Old
Modular forms	240	80	160
Cusp forms	208	80	128
Eisenstein series	32	0	32

Trace form

\( 80 q - 2 q^{2} - 42 q^{4} + 6 q^{5} + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
819.2.j.a	$819$	$2$	819.j	7.c	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None					273.2.i.a	$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
819.2.j.b	$819$	$2$	819.j	7.c	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None					91.2.e.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
819.2.j.c	$819$	$2$	819.j	7.c	$3$	$4$	$2$	$6.540$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					91.2.e.b	$2$	$1$	\(-3\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{2}+(3\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.d	$819$	$2$	819.j	7.c	$3$	$6$	$3$	$6.540$	6.0.64827.1	None					273.2.i.c	$2$	$0$	\(-2\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.e	$819$	$2$	819.j	7.c	$3$	$6$	$3$	$6.540$	\(\Q(\zeta_{18})\)	None					273.2.i.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
819.2.j.f	$819$	$2$	819.j	7.c	$3$	$8$	$4$	$6.540$	8.0.4868829729.1	None					273.2.i.d	$2$	$0$	\(-1\)	\(0\)	\(3\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(\beta _{3}+2\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
819.2.j.g	$819$	$2$	819.j	7.c	$3$	$10$	$5$	$6.540$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					273.2.i.e	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{8})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.h	$819$	$2$	819.j	7.c	$3$	$10$	$5$	$6.540$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					91.2.e.c	$2$	$0$	\(4\)	\(0\)	\(2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{7})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.i	$819$	$2$	819.j	7.c	$3$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			819.2.j.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{6})q^{2}+(-1-\beta _{5}-\beta _{9})q^{4}+\cdots\)
819.2.j.j	$819$	$2$	819.j	7.c	$3$	$20$	$10$	$6.540$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		819.2.j.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-2-2\beta _{3}-\beta _{14})q^{4}-\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)