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

• Label: 819.2.et
• Level: $819$
• Weight: $2$
• Character orbit: 819.et
• Rep. character: $\chi_{819}(136,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $180$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	480	196	284
Cusp forms	416	180	236
Eisenstein series	64	16	48

Trace form

\( 180 q + 2 q^{2} + 6 q^{5} + 2 q^{7} + 4 q^{8} + O(q^{10}) \)

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.et.a	$819$	$2$	819.et	91.aa	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+2\zeta_{12}^{3}q^{4}+(-1-2\zeta_{12}^{2})q^{7}+(-4\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.et.b	$819$	$2$	819.et	91.aa	$12$	$28$	$7$	$6.540$		None		$2$	$0$	\(2\)	\(0\)	\(6\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$
819.2.et.c	$819$	$2$	819.et	91.aa	$12$	$36$	$9$	$6.540$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{12}]$
819.2.et.d	$819$	$2$	819.et	91.aa	$12$	$40$	$10$	$6.540$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$
819.2.et.e	$819$	$2$	819.et	91.aa	$12$	$72$	$18$	$6.540$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$

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

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