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 + q^10 - 3 * q^11 + 14 * q^14 + 70 * q^16 + 22 * q^17 + 2 * q^19 + 6 * q^20 - 14 * q^22 - 10 * q^23 - 39 * q^25 - 28 * q^26 + 3 * q^28 + 4 * q^29 - 9 * q^31 + 46 * q^32 - 20 * q^34 - 15 * q^35 - 14 * q^37 - 8 * q^38 - 16 * q^40 - 7 * q^41 + 12 * q^43 + 2 * q^44 - 8 * q^46 - 10 * q^47 - 5 * q^49 - 17 * q^52 - 19 * q^53 + 26 * q^55 + 77 * q^56 - 7 * q^58 - 30 * q^59 + 14 * q^61 - 18 * q^62 - 8 * q^64 + 50 * q^65 + 10 * q^67 + 118 * q^68 - 2 * q^70 - 3 * q^71 + 3 * q^73 + 14 * q^74 - 10 * q^76 - 16 * q^77 - 20 * q^79 - 16 * q^80 + 22 * q^82 - 10 * q^83 + 13 * q^85 - 20 * q^86 - 9 * q^88 + 28 * q^89 + 65 * q^91 - 50 * q^92 + 8 * q^94 - 78 * q^95 + 40 * q^97 + 36 * q^98

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.s.a	$819$	$2$	819.s	91.h	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None					91.2.g.a	$2$	$0$	\(-2\)	\(0\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-q^{4}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
819.2.s.b	$819$	$2$	819.s	91.h	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None					273.2.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{4}+(-3+2\zeta_{6})q^{7}-6\zeta_{6}q^{11}+\cdots\)
819.2.s.c	$819$	$2$	819.s	91.h	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			819.2.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-2q^{4}+(-3+2\zeta_{6})q^{7}+(3-4\zeta_{6})q^{13}+\cdots\)
819.2.s.d	$819$	$2$	819.s	91.h	$3$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					91.2.g.b	$2$	$0$	\(4\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}-\beta _{5}+\beta _{11})q^{2}+(1-\beta _{6}-\beta _{10}+\cdots)q^{4}+\cdots\)
819.2.s.e	$819$	$2$	819.s	91.h	$3$	$16$	$8$	$6.540$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					273.2.j.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(1+\beta _{3}-\beta _{4})q^{4}+\beta _{14}q^{5}+\cdots\)
819.2.s.f	$819$	$2$	819.s	91.h	$3$	$20$	$10$	$6.540$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					273.2.j.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}-\beta _{10}q^{5}-\beta _{11}q^{7}+\cdots\)
819.2.s.g	$819$	$2$	819.s	91.h	$3$	$36$	$18$	$6.540$		None		✓	✓		819.2.n.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{3}]$

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

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