Space of modular forms of level 801, weight 2, and trivial character

• Label: 801.2.a
• Level: $801$
• Weight: $2$
• Character orbit: 801.a
• Rep. character: $\chi_{801}(1,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $11$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 801 = 3^{2} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	801.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(801))\).

	Total	New	Old
Modular forms	94	36	58
Cusp forms	87	36	51
Eisenstein series	7	0	7

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

\(3\)	\(89\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(7\)
\(+\)	\(-\)	$-$	\(7\)
\(-\)	\(+\)	$-$	\(14\)
\(-\)	\(-\)	$+$	\(8\)
Plus space		\(+\)	\(15\)
Minus space		\(-\)	\(21\)

Trace form

\( 36 q + 2 q^{2} + 32 q^{4} + 2 q^{5} - 2 q^{7} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(801))\) 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	89
801.2.a.a	$801$	$2$	801.a	1.a	$1$	$1$	$1$	$6.396$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+2q^{7}+3q^{8}-2q^{10}+\cdots\)
801.2.a.b	$801$	$2$	801.a	1.a	$1$	$1$	$1$	$6.396$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}-2q^{7}-2q^{11}+6q^{13}+\cdots\)
801.2.a.c	$801$	$2$	801.a	1.a	$1$	$1$	$1$	$6.396$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}-6q^{11}+2q^{13}+4q^{16}+\cdots\)
801.2.a.d	$801$	$2$	801.a	1.a	$1$	$1$	$1$	$6.396$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
801.2.a.e	$801$	$2$	801.a	1.a	$1$	$3$	$3$	$6.396$	3.3.169.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
801.2.a.f	$801$	$2$	801.a	1.a	$1$	$3$	$3$	$6.396$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
801.2.a.g	$801$	$2$	801.a	1.a	$1$	$3$	$3$	$6.396$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(7\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
801.2.a.h	$801$	$2$	801.a	1.a	$1$	$4$	$4$	$6.396$	4.4.23377.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
801.2.a.i	$801$	$2$	801.a	1.a	$1$	$5$	$5$	$6.396$	5.5.535120.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(3-\beta _{1}+\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
801.2.a.j	$801$	$2$	801.a	1.a	$1$	$7$	$7$	$6.396$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
801.2.a.k	$801$	$2$	801.a	1.a	$1$	$7$	$7$	$6.396$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(801))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(801)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 2}\)