Space of modular forms of level 833, weight 2, and Character 833.g

• Label: 833.2.g
• Level: $833$
• Weight: $2$
• Character orbit: 833.g
• Rep. character: $\chi_{833}(344,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $112$
• Newform subspaces: $9$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(833, [\chi])\).

	Total	New	Old
Modular forms	184	132	52
Cusp forms	152	112	40
Eisenstein series	32	20	12

Trace form

\( 112 q + 4 q^{3} - 96 q^{4} + 8 q^{5} - 4 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(833, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
833.2.g.a	$833$	$2$	833.g	17.c	$4$	$2$	$1$	$6.652$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}+(-2-2i)q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
833.2.g.b	$833$	$2$	833.g	17.c	$4$	$2$	$1$	$6.652$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}+(2+2i)q^{3}+q^{4}+(1+i)q^{5}+\cdots\)
833.2.g.c	$833$	$2$	833.g	17.c	$4$	$4$	$2$	$6.652$	\(\Q(i, \sqrt{11})\)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
833.2.g.d	$833$	$2$	833.g	17.c	$4$	$4$	$2$	$6.652$	\(\Q(i, \sqrt{11})\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
833.2.g.e	$833$	$2$	833.g	17.c	$4$	$16$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{8}-\beta _{13})q^{2}+\beta _{9}q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
833.2.g.f	$833$	$2$	833.g	17.c	$4$	$16$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
833.2.g.g	$833$	$2$	833.g	17.c	$4$	$16$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
833.2.g.h	$833$	$2$	833.g	17.c	$4$	$20$	$10$	$6.652$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{14}q^{3}+(-2+\beta _{17}+\beta _{18}+\cdots)q^{4}+\cdots\)
833.2.g.i	$833$	$2$	833.g	17.c	$4$	$32$	$16$	$6.652$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(833, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(833, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)