Space of modular forms of level 867, weight 2, and Character 867.e

• Label: 867.2.e
• Level: $867$
• Weight: $2$
• Character orbit: 867.e
• Rep. character: $\chi_{867}(616,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $11$
• Sturm bound: $204$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(204\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(867, [\chi])\).

	Total	New	Old
Modular forms	240	88	152
Cusp forms	168	88	80
Eisenstein series	72	0	72

Trace form

\( 88 q - 84 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(867, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
867.2.e.a	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-2\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-2q^{4}+3\zeta_{8}q^{5}+\cdots\)
867.2.e.b	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
867.2.e.c	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}-\zeta_{8}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
867.2.e.d	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}+q^{4}-\zeta_{8}q^{6}+\cdots\)
867.2.e.e	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+2q^{4}+3\zeta_{8}q^{5}+4\zeta_{8}^{3}q^{7}+\cdots\)
867.2.e.f	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	8.0.5473632256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}+\beta _{7}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots\)
867.2.e.g	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	8.0.836829184.2	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
867.2.e.h	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{16}^{4}-\zeta_{16}^{7})q^{2}-\zeta_{16}q^{3}+(-\zeta_{16}+\cdots)q^{4}+\cdots\)
867.2.e.i	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{16}^{4}-\zeta_{16}^{7})q^{2}+\zeta_{16}q^{3}+(-\zeta_{16}+\cdots)q^{4}+\cdots\)
867.2.e.j	$867$	$2$	867.e	17.c	$4$	$12$	$6$	$6.923$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{7}+\beta _{9})q^{2}+\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\)
867.2.e.k	$867$	$2$	867.e	17.c	$4$	$24$	$12$	$6.923$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(867, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(867, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)