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 - 2 * q^10 + 6 * q^11 + 14 * q^14 - 35 * q^16 - 11 * q^17 - 4 * q^19 + 6 * q^20 - 14 * q^22 + 5 * q^23 - 39 * q^25 + 2 * q^26 - 12 * q^28 + 4 * q^29 - 9 * q^31 - 23 * q^32 - 20 * q^34 - 9 * q^35 + 7 * q^37 - 8 * q^38 - 16 * q^40 - 7 * q^41 + 12 * q^43 + 2 * q^44 + 4 * q^46 - 10 * q^47 - 26 * q^49 + 28 * q^52 - 19 * q^53 + 26 * q^55 - 31 * q^56 + 14 * q^58 + 15 * q^59 - 28 * q^61 - 18 * q^62 - 8 * q^64 + 8 * q^65 - 20 * q^67 - 59 * q^68 - 2 * q^70 - 3 * q^71 + 3 * q^73 - 7 * q^74 - 10 * q^76 - 16 * q^77 - 20 * q^79 + 32 * q^80 - 44 * q^82 - 10 * q^83 + 13 * q^85 - 20 * q^86 + 18 * q^88 - 14 * q^89 + 29 * q^91 - 50 * q^92 - 16 * q^94 + 39 * q^95 + 40 * q^97 + 33 * 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.n.a	$819$	$2$	819.n	91.g	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			819.2.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+(3-4\zeta_{6})q^{13}+\cdots\)
819.2.n.b	$819$	$2$	819.n	91.g	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None					273.2.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+6q^{11}+\cdots\)
819.2.n.c	$819$	$2$	819.n	91.g	$3$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None					91.2.g.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
819.2.n.d	$819$	$2$	819.n	91.g	$3$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					91.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}+(\beta _{6}-\beta _{7})q^{4}+\cdots\)
819.2.n.e	$819$	$2$	819.n	91.g	$3$	$16$	$8$	$6.540$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					273.2.j.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
819.2.n.f	$819$	$2$	819.n	91.g	$3$	$20$	$10$	$6.540$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					273.2.j.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}-2\beta _{7}-\beta _{16}+\cdots)q^{4}+\cdots\)
819.2.n.g	$819$	$2$	819.n	91.g	$3$	$36$	$18$	$6.540$		None		✓	✓		819.2.n.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{3}]$

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

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