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

• Label: 819.2.g
• Level: $819$
• Weight: $2$
• Character orbit: 819.g
• Rep. character: $\chi_{819}(818,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	120	40	80
Cusp forms	104	40	64
Eisenstein series	16	0	16

Trace form

\( 40 q + 48 q^{4} + O(q^{10}) \)

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.g.a	$819$	$2$	819.g	273.g	$2$	$8$	$8$	$6.540$	8.0.\(\cdots\).5	\(\Q(\sqrt{-91}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}+\beta _{5}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{13}+\cdots\)
819.2.g.b	$819$	$2$	819.g	273.g	$2$	$8$	$8$	$6.540$	8.0.40960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+3q^{4}-2\beta _{1}q^{5}+(\beta _{2}+2\beta _{7})q^{7}+\cdots\)
819.2.g.c	$819$	$2$	819.g	273.g	$2$	$12$	$12$	$6.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{5})q^{2}+(2-\beta _{1}-\beta _{5})q^{4}+\cdots\)
819.2.g.d	$819$	$2$	819.g	273.g	$2$	$12$	$12$	$6.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{5})q^{2}+(2-\beta _{1}-\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots\)

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

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