Space of modular forms of level 891, weight 2, and trivial character

• Label: 891.2.a
• Level: $891$
• Weight: $2$
• Character orbit: 891.a
• Rep. character: $\chi_{891}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $18$
• Sturm bound: $216$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(216\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(891))\).

	Total	New	Old
Modular forms	120	40	80
Cusp forms	97	40	57
Eisenstein series	23	0	23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(-\)	$-$	\(13\)
\(-\)	\(+\)	$-$	\(11\)
\(-\)	\(-\)	$+$	\(7\)
Plus space		\(+\)	\(16\)
Minus space		\(-\)	\(24\)

Trace form

\( 40 q + 40 q^{4} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(891))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11
891.2.a.a	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.b	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.c	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.d	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}-4q^{7}+q^{11}+2q^{13}+\cdots\)
891.2.a.e	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots\)
891.2.a.f	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.g	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.h	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.i	$891$	$2$	891.a	1.a	$1$	$2$	$2$	$7.115$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.j	$891$	$2$	891.a	1.a	$1$	$2$	$2$	$7.115$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.k	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.l	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.m	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	3.3.837.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
891.2.a.n	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	3.3.837.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
891.2.a.o	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.4752.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-8\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
891.2.a.p	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.22545.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
891.2.a.q	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.22545.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(4\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
891.2.a.r	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.4752.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(8\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(891))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(891)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 2}\)