Space of modular forms of level 449, weight 2, and trivial character

• Label: 449.2.a
• Level: $449$
• Weight: $2$
• Character orbit: 449.a
• Rep. character: $\chi_{449}(1,\cdot)$
• Character field: $\Q$
• Dimension: $37$
• Newform subspaces: $2$
• Sturm bound: $75$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 449 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	449.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(75\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(449))\).

	Total	New	Old
Modular forms	38	38	0
Cusp forms	37	37	0
Eisenstein series	1	1	0

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

\(449\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(14\)	\(14\)	\(0\)		\(14\)	\(14\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(24\)	\(24\)	\(0\)		\(23\)	\(23\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

37 * q - 3 * q^2 - 2 * q^3 + 37 * q^4 - 4 * q^5 - 6 * q^6 + 4 * q^7 - 9 * q^8 + 27 * q^9 - 4 * q^10 - 8 * q^11 - 12 * q^12 - 4 * q^14 - 16 * q^15 + 25 * q^16 - 6 * q^17 - 7 * q^18 + 2 * q^19 - 4 * q^20 - 2 * q^21 - 10 * q^22 - 4 * q^23 - 2 * q^24 + 37 * q^25 + 8 * q^26 - 8 * q^27 - 10 * q^29 + 14 * q^30 + 16 * q^31 - q^32 + 14 * q^33 - 14 * q^34 + 14 * q^35 + 29 * q^36 + 4 * q^37 + 38 * q^38 + 2 * q^40 - 14 * q^41 + 22 * q^42 + 12 * q^43 - 38 * q^44 - 28 * q^45 + 22 * q^46 + 24 * q^47 - 40 * q^48 + 45 * q^49 - 35 * q^50 + 12 * q^51 - 20 * q^52 + 6 * q^53 - 18 * q^54 - 14 * q^55 - 4 * q^56 - 28 * q^57 + 12 * q^58 - 18 * q^59 - 8 * q^60 - 2 * q^61 - 10 * q^62 + 16 * q^63 - 5 * q^64 - 26 * q^65 + 22 * q^66 + 6 * q^67 - 38 * q^68 - 6 * q^69 - 2 * q^70 - 14 * q^71 - 43 * q^72 + 24 * q^73 - 22 * q^74 + 10 * q^75 + 32 * q^76 + 26 * q^77 + 6 * q^78 + 22 * q^79 + 18 * q^80 - 19 * q^81 + 6 * q^82 + 36 * q^83 - 52 * q^84 + 6 * q^85 - 56 * q^86 + 18 * q^87 - 52 * q^88 - 42 * q^89 - 22 * q^90 - 8 * q^91 - 50 * q^92 - 26 * q^93 - 54 * q^94 + 32 * q^95 + 8 * q^96 - 14 * q^97 + 15 * q^98 - 38 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(449))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		449
449.2.a.a	$449$	$2$	449.a	1.a	$1$	$14$	$14$	$3.585$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓	✓	449.2.a.a	$1$	$1$	\(-3\)	\(-5\)	\(-7\)	\(-22\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2}+\beta _{3})q^{4}+\cdots\)
449.2.a.b	$449$	$2$	449.a	1.a	$1$	$23$	$23$	$3.585$		None	✓	✓	✓	✓	449.2.a.b	$1$	$0$	\(0\)	\(3\)	\(3\)	\(26\)		$-$	$-$		$\mathrm{SU}(2)$