Space of modular forms of level 479, weight 2, and trivial character

• Label: 479.2.a
• Level: $479$
• Weight: $2$
• Character orbit: 479.a
• Rep. character: $\chi_{479}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 479 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	479.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(479))\).

	Total	New	Old
Modular forms	41	41	0
Cusp forms	40	40	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.

\(479\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(8\)	\(8\)	\(0\)		\(8\)	\(8\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(33\)	\(33\)	\(0\)		\(32\)	\(32\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

40 * q + q^2 + 2 * q^3 + 43 * q^4 + 2 * q^5 + 6 * q^6 + 4 * q^7 + 3 * q^8 + 48 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^14 + 6 * q^15 + 53 * q^16 - 4 * q^17 + 9 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^21 - 4 * q^22 + 2 * q^24 + 54 * q^25 - 4 * q^26 + 8 * q^27 + 12 * q^29 - 34 * q^30 + 18 * q^31 - 13 * q^32 + 6 * q^33 + 6 * q^34 - 16 * q^35 + 49 * q^36 + 28 * q^37 - 16 * q^38 + 20 * q^39 - 16 * q^40 + 12 * q^41 - 58 * q^42 - 8 * q^43 + 28 * q^44 - 2 * q^45 + 42 * q^46 - 14 * q^47 - 6 * q^48 + 62 * q^49 - 27 * q^50 - 20 * q^51 - 14 * q^52 + 4 * q^53 - 20 * q^54 - 2 * q^55 - 32 * q^56 + 6 * q^57 + 44 * q^58 - 2 * q^59 - 38 * q^60 + 22 * q^61 - 36 * q^62 - 24 * q^63 + 87 * q^64 + 26 * q^65 - 96 * q^66 + 16 * q^67 - 36 * q^68 + 6 * q^69 - 2 * q^70 + 14 * q^71 - 31 * q^72 + 38 * q^73 - 16 * q^74 + 8 * q^75 - 22 * q^76 - 48 * q^77 - 90 * q^78 + 36 * q^79 - 50 * q^80 + 88 * q^81 + 2 * q^82 - 34 * q^83 - 74 * q^84 + 38 * q^85 - 36 * q^86 - 64 * q^87 + 16 * q^88 + 48 * q^89 - 132 * q^90 + 30 * q^91 - 74 * q^92 + 32 * q^93 - 4 * q^94 - 76 * q^95 - 90 * q^96 + 60 * q^97 - 43 * q^98 - 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(479))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		479
479.2.a.a	$479$	$2$	479.a	1.a	$1$	$8$	$8$	$3.825$	8.8.1653760901.1	None	✓	✓	✓	✓	479.2.a.a	$1$	$1$	\(-2\)	\(-3\)	\(-4\)	\(-4\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
479.2.a.b	$479$	$2$	479.a	1.a	$1$	$32$	$32$	$3.825$		None	✓	✓	✓	✓	479.2.a.b	$1$	$0$	\(3\)	\(5\)	\(6\)	\(8\)		$-$	$-$		$\mathrm{SU}(2)$