Space of modular forms of level 447, weight 2, and trivial character

• Label: 447.2.a
• Level: $447$
• Weight: $2$
• Character orbit: 447.a
• Rep. character: $\chi_{447}(1,\cdot)$
• Character field: $\Q$
• Dimension: $25$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 447 = 3 \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	447.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(100\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(447))\).

	Total	New	Old
Modular forms	52	25	27
Cusp forms	49	25	24
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.

\(3\)	\(149\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	$-$	\(10\)
\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(6\)
Minus space		\(-\)	\(19\)

Trace form

\( 25 q + 3 q^{2} - q^{3} + 25 q^{4} + 6 q^{5} - q^{6} + 4 q^{7} + 15 q^{8} + 25 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(447))\) 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	149
447.2.a.a	$447$	$2$	447.a	1.a	$1$	$3$	$3$	$3.569$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(-3\)	\(3\)	\(-6\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
447.2.a.b	$447$	$2$	447.a	1.a	$1$	$3$	$3$	$3.569$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots\)
447.2.a.c	$447$	$2$	447.a	1.a	$1$	$9$	$9$	$3.569$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(9\)	\(8\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{6}+\cdots)q^{5}+\cdots\)
447.2.a.d	$447$	$2$	447.a	1.a	$1$	$10$	$10$	$3.569$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-10\)	\(4\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(447))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(447)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 2}\)