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

• Label: 819.2.n
• Level: $819$
• Weight: $2$
• Character orbit: 819.n
• Rep. character: $\chi_{819}(100,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $90$
• Newform subspaces: $7$
• Sturm bound: $224$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(224\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	240	98	142
Cusp forms	208	90	118
Eisenstein series	32	8	24

Trace form

\( 90 q - q^{2} - 43 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
819.2.n.a	$819$	$2$	819.n	91.g	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+(3-4\zeta_{6})q^{13}+\cdots\)
819.2.n.b	$819$	$2$	819.n	91.g	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+6q^{11}+\cdots\)
819.2.n.c	$819$	$2$	819.n	91.g	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
819.2.n.d	$819$	$2$	819.n	91.g	$3$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}+(\beta _{6}-\beta _{7})q^{4}+\cdots\)
819.2.n.e	$819$	$2$	819.n	91.g	$3$	$16$	$8$	$6.540$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
819.2.n.f	$819$	$2$	819.n	91.g	$3$	$20$	$10$	$6.540$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}-2\beta _{7}-\beta _{16}+\cdots)q^{4}+\cdots\)
819.2.n.g	$819$	$2$	819.n	91.g	$3$	$36$	$18$	$6.540$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{3}]$

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

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