Space of modular forms of level 892, weight 2, and trivial character

• Label: 892.2.a
• Level: $892$
• Weight: $2$
• Character orbit: 892.a
• Rep. character: $\chi_{892}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 892 = 2^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	892.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(892))\).

	Total	New	Old
Modular forms	115	18	97
Cusp forms	110	18	92
Eisenstein series	5	0	5

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

\(2\)	\(223\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	$+$	\(9\)
Plus space		\(+\)	\(9\)
Minus space		\(-\)	\(9\)

Trace form

\( 18 q - 2 q^{3} + 2 q^{7} + 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(892))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	223
892.2.a.a	$892$	$2$	892.a	1.a	$1$	$1$	$1$	$7.123$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}-2q^{9}-3q^{11}+\cdots\)
892.2.a.b	$892$	$2$	892.a	1.a	$1$	$1$	$1$	$7.123$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots\)
892.2.a.c	$892$	$2$	892.a	1.a	$1$	$1$	$1$	$7.123$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{7}+6q^{9}+q^{11}-3q^{17}+\cdots\)
892.2.a.d	$892$	$2$	892.a	1.a	$1$	$7$	$7$	$7.123$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-7\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{6})q^{5}+\cdots\)
892.2.a.e	$892$	$2$	892.a	1.a	$1$	$8$	$8$	$7.123$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(\beta _{2}-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(892))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(892)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 2}\)