Space of modular forms of level 891, weight 2, and Character 891.n

• Label: 891.2.n
• Level: $891$
• Weight: $2$
• Character orbit: 891.n
• Rep. character: $\chi_{891}(136,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $368$
• Newform subspaces: $12$
• Sturm bound: $216$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(216\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(891, [\chi])\).

	Total	New	Old
Modular forms	960	400	560
Cusp forms	768	368	400
Eisenstein series	192	32	160

Trace form

368 * q + 50 * q^4 + 6 * q^7 - 16 * q^10 + 6 * q^13 + 38 * q^16 - 48 * q^19 - 2 * q^22 + 38 * q^25 + 36 * q^28 - 4 * q^34 + 2 * q^40 + 4 * q^43 - 36 * q^46 + 40 * q^49 - 18 * q^52 - 56 * q^55 - 92 * q^58 + 6 * q^61 - 68 * q^64 + 28 * q^67 + 80 * q^70 + 60 * q^73 - 44 * q^76 + 42 * q^79 - 32 * q^82 - 38 * q^85 - 278 * q^88 - 28 * q^91 + 118 * q^94 + 54 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(891, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
891.2.n.a	$891$	$2$	891.n	99.m	$15$	$8$	$1$	$7.115$	\(\Q(\zeta_{15})\)	None					33.2.e.a	$4$	$0$	\(-3\)	\(0\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\zeta_{15}^{2}+\zeta_{15}^{5})q^{2}+(-1+\zeta_{15}^{4}+\cdots)q^{4}+\cdots\)
891.2.n.b	$891$	$2$	891.n	99.m	$15$	$8$	$1$	$7.115$	\(\Q(\zeta_{15})\)	None					33.2.e.b	$4$	$0$	\(-1\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-2\zeta_{15}+\zeta_{15}^{2}+\zeta_{15}^{5}-2\zeta_{15}^{6}+\cdots)q^{2}+\cdots\)
891.2.n.c	$891$	$2$	891.n	99.m	$15$	$8$	$1$	$7.115$	\(\Q(\zeta_{15})\)	None					33.2.e.b	$4$	$0$	\(1\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+2\zeta_{15}^{6}+\cdots)q^{2}+\cdots\)
891.2.n.d	$891$	$2$	891.n	99.m	$15$	$8$	$1$	$7.115$	\(\Q(\zeta_{15})\)	None					33.2.e.a	$4$	$0$	\(3\)	\(0\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-\zeta_{15}^{2}-\zeta_{15}^{5})q^{2}+(-1+\zeta_{15}^{4}+\cdots)q^{4}+\cdots\)
891.2.n.e	$891$	$2$	891.n	99.m	$15$	$16$	$2$	$7.115$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					99.2.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+\beta _{1}q^{2}+(2\beta _{2}-\beta _{9}-\beta _{11})q^{4}-\beta _{13}q^{5}+\cdots\)
891.2.n.f	$891$	$2$	891.n	99.m	$15$	$32$	$4$	$7.115$		None					297.2.f.a	$4$	$0$	\(-2\)	\(0\)	\(-1\)	\(2\)		$\mathrm{SU}(2)[C_{15}]$
891.2.n.g	$891$	$2$	891.n	99.m	$15$	$32$	$4$	$7.115$		None					297.2.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{15}]$
891.2.n.h	$891$	$2$	891.n	99.m	$15$	$32$	$4$	$7.115$		None					297.2.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{15}]$
891.2.n.i	$891$	$2$	891.n	99.m	$15$	$32$	$4$	$7.115$		None					297.2.f.a	$4$	$0$	\(2\)	\(0\)	\(1\)	\(2\)		$\mathrm{SU}(2)[C_{15}]$
891.2.n.j	$891$	$2$	891.n	99.m	$15$	$48$	$6$	$7.115$		None		✓			891.2.f.c	$4$	$0$	\(-2\)	\(0\)	\(4\)	\(-7\)		$\mathrm{SU}(2)[C_{15}]$
891.2.n.k	$891$	$2$	891.n	99.m	$15$	$48$	$6$	$7.115$		None		✓			891.2.f.c	$4$	$0$	\(2\)	\(0\)	\(-4\)	\(-7\)		$\mathrm{SU}(2)[C_{15}]$
891.2.n.l	$891$	$2$	891.n	99.m	$15$	$96$	$12$	$7.115$		None		✓	✓		891.2.f.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(14\)		$\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(891, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(891, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)