Space of modular forms of level 893, weight 2, and trivial character

• Label: 893.2.a
• Level: $893$
• Weight: $2$
• Character orbit: 893.a
• Rep. character: $\chi_{893}(1,\cdot)$
• Character field: $\Q$
• Dimension: $69$
• Newform subspaces: $4$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 893 = 19 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	893.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(893))\).

	Total	New	Old
Modular forms	82	69	13
Cusp forms	79	69	10
Eisenstein series	3	0	3

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

\(19\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(16\)
\(+\)	\(-\)	$-$	\(18\)
\(-\)	\(+\)	$-$	\(23\)
\(-\)	\(-\)	$+$	\(12\)
Plus space		\(+\)	\(28\)
Minus space		\(-\)	\(41\)

Trace form

\( 69 q - 3 q^{2} + 4 q^{3} + 69 q^{4} - 2 q^{5} + 8 q^{6} - 4 q^{7} - 3 q^{8} + 77 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(893))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		19	47
893.2.a.a	$893$	$2$	893.a	1.a	$1$	$12$	$12$	$7.131$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-9\)	\(-7\)	\(-13\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
893.2.a.b	$893$	$2$	893.a	1.a	$1$	$16$	$16$	$7.131$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(-13\)	\(-1\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
893.2.a.c	$893$	$2$	893.a	1.a	$1$	$18$	$18$	$7.131$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(13\)	\(5\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
893.2.a.d	$893$	$2$	893.a	1.a	$1$	$23$	$23$	$7.131$		None	✓	$1$	$0$	\(1\)	\(13\)	\(1\)	\(15\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(893))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(893)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 2}\)