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

• Label: 819.2.fm
• Level: $819$
• Weight: $2$
• Character orbit: 819.fm
• Rep. character: $\chi_{819}(370,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $176$
• Newform subspaces: $8$
• Sturm bound: $224$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(224\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	480	192	288
Cusp forms	416	176	240
Eisenstein series	64	16	48

Trace form

\( 176 q + 8 q^{2} - 12 q^{4} - 4 q^{7} + 16 q^{8} + O(q^{10}) \)

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.fm.a	$819$	$2$	819.fm	91.ac	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
819.2.fm.b	$819$	$2$	819.fm	91.ac	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
819.2.fm.c	$819$	$2$	819.fm	91.ac	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q-2\zeta_{12}q^{4}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+(3\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.fm.d	$819$	$2$	819.fm	91.ac	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q-2\zeta_{12}q^{4}+(2+\zeta_{12}^{2})q^{7}+(-3\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.fm.e	$819$	$2$	819.fm	91.ac	$12$	$32$	$8$	$6.540$		None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$
819.2.fm.f	$819$	$2$	819.fm	91.ac	$12$	$32$	$8$	$6.540$		None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$
819.2.fm.g	$819$	$2$	819.fm	91.ac	$12$	$32$	$8$	$6.540$		None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
819.2.fm.h	$819$	$2$	819.fm	91.ac	$12$	$64$	$16$	$6.540$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$

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

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