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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(7\)	\(1\)	\(6\)		\(7\)	\(1\)	\(6\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(22\)	\(9\)	\(13\)		\(21\)	\(9\)	\(12\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(15\)	\(8\)	\(7\)		\(14\)	\(8\)	\(6\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(14\)	\(1\)	\(13\)		\(13\)	\(1\)	\(12\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(21\)	\(2\)	\(19\)		\(20\)	\(2\)	\(18\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(37\)	\(17\)	\(20\)		\(35\)	\(17\)	\(18\)		\(2\)	\(0\)	\(2\)

Trace form

19 * q - q^2 + 2 * q^3 + 19 * q^4 + 2 * q^6 + 4 * q^7 - q^8 + 27 * q^9 + 2 * q^11 + 2 * q^12 + 4 * q^13 + 4 * q^14 + 16 * q^15 + 19 * q^16 + 2 * q^17 - 13 * q^18 + 12 * q^19 + 12 * q^21 + 6 * q^22 - 4 * q^23 + 2 * q^24 + 37 * q^25 + 20 * q^27 + 4 * q^28 + 10 * q^29 + 12 * q^31 - q^32 - 12 * q^33 - 18 * q^34 - 8 * q^35 + 27 * q^36 + 10 * q^37 - 12 * q^38 + 8 * q^39 - 14 * q^41 - 12 * q^42 + 8 * q^43 + 2 * q^44 - 20 * q^45 + 12 * q^46 - 4 * q^47 + 2 * q^48 + 35 * q^49 - 23 * q^50 + 8 * q^51 + 4 * q^52 - 26 * q^53 - 16 * q^54 + 16 * q^55 + 4 * q^56 - 16 * q^57 + 6 * q^58 - 10 * q^59 + 16 * q^60 + 48 * q^61 + 4 * q^62 - 48 * q^63 + 19 * q^64 - 44 * q^65 - 40 * q^66 + 22 * q^67 + 2 * q^68 - 4 * q^69 + 8 * q^70 + 4 * q^71 - 13 * q^72 - 22 * q^73 - 26 * q^74 - 42 * q^75 + 12 * q^76 - 48 * q^77 - 32 * q^78 + 44 * q^79 + 27 * q^81 - 26 * q^82 - 40 * q^83 + 12 * q^84 - 28 * q^85 + 8 * q^86 - 80 * q^87 + 6 * q^88 - 6 * q^89 - 40 * q^90 + 24 * q^91 - 4 * q^92 - 56 * q^93 + 4 * q^94 - 48 * q^95 + 2 * q^96 + 10 * q^97 - 49 * q^98 - 58 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓			446.2.a.a	$1$	$2$	\(-1\)	\(-3\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-4q^{5}+3q^{6}-4q^{7}+\cdots\)
446.2.a.b	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	✓	✓	✓	446.2.a.b	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
446.2.a.c	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	✓	✓	✓	446.2.a.c	$1$	$1$	\(1\)	\(-1\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
446.2.a.d	$446$	$2$	446.a	1.a	$1$	$1$	$1$	$3.561$	\(\Q\)	None	✓	✓			446.2.a.d	$1$	$0$	\(1\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
446.2.a.e	$446$	$2$	446.a	1.a	$1$	$7$	$7$	$3.561$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		446.2.a.e	$1$	$0$	\(7\)	\(1\)	\(2\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
446.2.a.f	$446$	$2$	446.a	1.a	$1$	$8$	$8$	$3.561$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		446.2.a.f	$1$	$0$	\(-8\)	\(4\)	\(4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)

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

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