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

• Label: 819.2.fn
• Level: $819$
• Weight: $2$
• Character orbit: 819.fn
• Rep. character: $\chi_{819}(73,\cdot)$
• 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.fn (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 \(T_p\):			\(2\), \(19\)

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

\( 176 q + 2 q^{2} + 6 q^{5} - 10 q^{7} + 16 q^{8} + O(q^{10}) \)

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.fn.a	$819$	$2$	819.fn	91.ab	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+2\zeta_{12}q^{4}+(-2+3\zeta_{12}^{2})q^{7}+(-\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.fn.b	$819$	$2$	819.fn	91.ab	$12$	$4$	$1$	$6.540$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+2\zeta_{12}q^{4}+(3\zeta_{12}-\zeta_{12}^{3})q^{7}+(-\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.fn.c	$819$	$2$	819.fn	91.ab	$12$	$8$	$2$	$6.540$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{6}q^{2}+(-2+2\beta _{3}-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
819.2.fn.d	$819$	$2$	819.fn	91.ab	$12$	$8$	$2$	$6.540$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{5}q^{2}+(1+2\beta _{2}-\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
819.2.fn.e	$819$	$2$	819.fn	91.ab	$12$	$32$	$8$	$6.540$		None		$4$	$0$	\(2\)	\(0\)	\(6\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$
819.2.fn.f	$819$	$2$	819.fn	91.ab	$12$	$36$	$9$	$6.540$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$
819.2.fn.g	$819$	$2$	819.fn	91.ab	$12$	$36$	$9$	$6.540$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$
819.2.fn.h	$819$	$2$	819.fn	91.ab	$12$	$48$	$12$	$6.540$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

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

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