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

• Label: 867.2.h
• Level: $867$
• Weight: $2$
• Character orbit: 867.h
• Rep. character: $\chi_{867}(688,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $184$
• Newform subspaces: $13$
• Sturm bound: $204$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(204\)
Trace bound:			\(16\)
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	480	184	296
Cusp forms	336	184	152
Eisenstein series	144	0	144

Trace form

184 * q + 8 * q^5 + 8 * q^6 - 8 * q^11 + 16 * q^14 - 208 * q^16 + 8 * q^19 - 16 * q^20 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 - 16 * q^26 + 8 * q^28 - 8 * q^31 - 64 * q^35 - 8 * q^36 + 8 * q^37 - 16 * q^39 + 8 * q^40 + 24 * q^41 - 8 * q^42 + 8 * q^43 + 8 * q^45 + 8 * q^49 + 64 * q^50 - 16 * q^52 + 32 * q^53 + 8 * q^54 + 16 * q^56 + 16 * q^57 - 24 * q^58 - 16 * q^59 + 8 * q^60 - 16 * q^61 - 16 * q^62 - 24 * q^65 + 16 * q^66 + 64 * q^67 + 16 * q^69 - 40 * q^70 + 16 * q^71 - 48 * q^73 - 64 * q^74 - 16 * q^75 - 24 * q^76 - 8 * q^78 + 16 * q^80 + 8 * q^82 - 32 * q^83 + 48 * q^84 - 24 * q^87 + 8 * q^88 + 16 * q^91 + 32 * q^92 + 32 * q^93 + 40 * q^95 + 16 * q^96 - 8 * q^97 - 8 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
867.2.h.a	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None		✓			867.2.a.g	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{16}^{4}-\zeta_{16}^{6})q^{2}+\zeta_{16}q^{3}+\cdots\)
867.2.h.b	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None					51.2.h.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{3}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)
867.2.h.c	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None					51.2.a.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{5}q^{3}+2\zeta_{16}^{4}q^{4}-3\zeta_{16}q^{5}+\cdots\)
867.2.h.d	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None					51.2.d.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{3}q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)
867.2.h.e	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None					51.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q-2\zeta_{16}^{6}q^{2}-\zeta_{16}q^{3}-2\zeta_{16}^{4}q^{4}+\cdots\)
867.2.h.f	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None					51.2.h.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{3}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)
867.2.h.g	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None					51.2.h.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)
867.2.h.h	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	\(\Q(\zeta_{16})\)	None		✓			867.2.a.g	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{16}^{4}-\zeta_{16}^{6})q^{2}-\zeta_{16}q^{3}+\cdots\)
867.2.h.i	$867$	$2$	867.h	17.d	$8$	$16$	$4$	$6.923$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					51.2.e.a	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{2}+\beta _{6})q^{2}+\beta _{15}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
867.2.h.j	$867$	$2$	867.h	17.d	$8$	$16$	$4$	$6.923$	16.0.\(\cdots\).1	None					51.2.a.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{3}+\beta _{5})q^{2}+\beta _{7}q^{3}+(3\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)
867.2.h.k	$867$	$2$	867.h	17.d	$8$	$16$	$4$	$6.923$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					51.2.e.a	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{13}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
867.2.h.l	$867$	$2$	867.h	17.d	$8$	$24$	$6$	$6.923$		None		✓			867.2.a.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
867.2.h.m	$867$	$2$	867.h	17.d	$8$	$48$	$12$	$6.923$		None		✓	✓		867.2.a.o	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(867, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)