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

• Label: 819.2.y
• Level: $819$
• Weight: $2$
• Character orbit: 819.y
• Rep. character: $\chi_{819}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $92$
• Newform subspaces: $9$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.y (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	240	100	140
Cusp forms	208	92	116
Eisenstein series	32	8	24

Trace form

\( 92 q + 4 q^{2} - 4 q^{8} + O(q^{10}) \)

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.y.a	$819$	$2$	819.y	91.i	$4$	$4$	$2$	$6.540$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-2+2\beta _{2})q^{5}+\cdots\)
819.2.y.b	$819$	$2$	819.y	91.i	$4$	$4$	$2$	$6.540$	\(\Q(i, \sqrt{10})\)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
819.2.y.c	$819$	$2$	819.y	91.i	$4$	$4$	$2$	$6.540$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+2\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
819.2.y.d	$819$	$2$	819.y	91.i	$4$	$4$	$2$	$6.540$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-2\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
819.2.y.e	$819$	$2$	819.y	91.i	$4$	$8$	$4$	$6.540$	8.0.\(\cdots\).3	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{6})q^{7}+\cdots\)
819.2.y.f	$819$	$2$	819.y	91.i	$4$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+(-1+\cdots)q^{5}+\cdots\)
819.2.y.g	$819$	$2$	819.y	91.i	$4$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(12\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+(1+\cdots)q^{5}+\cdots\)
819.2.y.h	$819$	$2$	819.y	91.i	$4$	$12$	$6$	$6.540$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}+(\beta _{4}-\beta _{6}-\beta _{7}-\beta _{8})q^{4}+\cdots\)
819.2.y.i	$819$	$2$	819.y	91.i	$4$	$32$	$16$	$6.540$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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