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

• Label: 819.2.c
• Level: $819$
• Weight: $2$
• Character orbit: 819.c
• Rep. character: $\chi_{819}(64,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
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	34	86
Cusp forms	104	34	70
Eisenstein series	16	0	16

Trace form

\( 34 q - 32 q^{4} + O(q^{10}) \)

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.c.a	$819$	$2$	819.c	13.b	$2$	$2$	$2$	$6.540$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+3iq^{5}+iq^{7}-6q^{10}+\cdots\)
819.2.c.b	$819$	$2$	819.c	13.b	$2$	$6$	$6$	$6.540$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.c.c	$819$	$2$	819.c	13.b	$2$	$6$	$6$	$6.540$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
819.2.c.d	$819$	$2$	819.c	13.b	$2$	$8$	$8$	$6.540$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\beta _{7})q^{5}+\cdots\)
819.2.c.e	$819$	$2$	819.c	13.b	$2$	$12$	$12$	$6.540$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-1+\beta _{10})q^{4}-\beta _{1}q^{5}+\cdots\)

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

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