Space of modular forms of level 446, weight 2, and trivial character

• Label: 446.2.a
• Level: $446$
• Weight: $2$
• Character orbit: 446.a
• Rep. character: $\chi_{446}(1,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $6$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 446 = 2 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	446.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(446))\).

	Total	New	Old
Modular forms	58	19	39
Cusp forms	55	19	36
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.

\(2\)	\(223\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(17\)

Trace form

\( 19 q - q^{2} + 2 q^{3} + 19 q^{4} + 2 q^{6} + 4 q^{7} - q^{8} + 27 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(446))\) 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
446.2.a.a	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	$1$	$2$	\(-1\)	\(-3\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-4q^{5}+3q^{6}-4q^{7}+\cdots\)
446.2.a.b	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
446.2.a.c	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
446.2.a.d	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
446.2.a.e	$446$	$2$	446.a	1.a	$1$	$7$	$7$	$3.561$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(1\)	\(2\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
446.2.a.f	$446$	$2$	446.a	1.a	$1$	$8$	$8$	$3.561$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(-8\)	\(4\)	\(4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(446))\) into lower level spaces

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