Space of modular forms of level 445, weight 2, and trivial character

• Label: 445.2.a
• Level: $445$
• Weight: $2$
• Character orbit: 445.a
• Rep. character: $\chi_{445}(1,\cdot)$
• Character field: $\Q$
• Dimension: $29$
• Newform subspaces: $7$
• Sturm bound: $90$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 445 = 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	445.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(90\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(445))\).

	Total	New	Old
Modular forms	46	29	17
Cusp forms	43	29	14
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.

\(5\)	\(89\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(8\)
\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	$+$	\(7\)
Plus space		\(+\)	\(13\)
Minus space		\(-\)	\(16\)

Trace form

\( 29 q - q^{2} + 23 q^{4} + q^{5} - 4 q^{6} - 8 q^{7} - 9 q^{8} + 33 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(445))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	89
445.2.a.a	$445$	$2$	445.a	1.a	$1$	$2$	$2$	$3.553$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta )q^{3}-q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
445.2.a.b	$445$	$2$	445.a	1.a	$1$	$2$	$2$	$3.553$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(3+\beta )q^{6}+\cdots\)
445.2.a.c	$445$	$2$	445.a	1.a	$1$	$2$	$2$	$3.553$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
445.2.a.d	$445$	$2$	445.a	1.a	$1$	$4$	$4$	$3.553$	4.4.725.1	None	✓	$1$	$1$	\(1\)	\(-2\)	\(-4\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+\cdots\)
445.2.a.e	$445$	$2$	445.a	1.a	$1$	$4$	$4$	$3.553$	4.4.8069.1	None	✓	$1$	$0$	\(1\)	\(4\)	\(4\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
445.2.a.f	$445$	$2$	445.a	1.a	$1$	$7$	$7$	$3.553$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(-8\)	\(7\)	\(-16\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{5})q^{3}+(2+\cdots)q^{4}+\cdots\)
445.2.a.g	$445$	$2$	445.a	1.a	$1$	$8$	$8$	$3.553$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(6\)	\(-8\)	\(-6\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 2}\)