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

• Label: 819.2.s
• Level: $819$
• Weight: $2$
• Character orbit: 819.s
• Rep. character: $\chi_{819}(289,\cdot)$
• 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.s (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

\( 90 q + 2 q^{2} + 86 q^{4} + 2 q^{5} + q^{7} + 12 q^{8} + O(q^{10}) \)

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.s.a	$819$	$2$	819.s	91.h	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-q^{4}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
819.2.s.b	$819$	$2$	819.s	91.h	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{4}+(-3+2\zeta_{6})q^{7}-6\zeta_{6}q^{11}+\cdots\)
819.2.s.c	$819$	$2$	819.s	91.h	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-2q^{4}+(-3+2\zeta_{6})q^{7}+(3-4\zeta_{6})q^{13}+\cdots\)
819.2.s.d	$819$	$2$	819.s	91.h	$3$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(4\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}-\beta _{5}+\beta _{11})q^{2}+(1-\beta _{6}-\beta _{10}+\cdots)q^{4}+\cdots\)
819.2.s.e	$819$	$2$	819.s	91.h	$3$	$16$	$8$	$6.540$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(1+\beta _{3}-\beta _{4})q^{4}+\beta _{14}q^{5}+\cdots\)
819.2.s.f	$819$	$2$	819.s	91.h	$3$	$20$	$10$	$6.540$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}-\beta _{10}q^{5}-\beta _{11}q^{7}+\cdots\)
819.2.s.g	$819$	$2$	819.s	91.h	$3$	$36$	$18$	$6.540$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{3}]$

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

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