Space of modular forms of level 2671, weight 2, and trivial character

• Label: 2671.2.a
• Level: $2671$
• Weight: $2$
• Character orbit: 2671.a
• Rep. character: $\chi_{2671}(1,\cdot)$
• Character field: $\Q$
• Dimension: $222$
• Newform subspaces: $2$
• Sturm bound: $445$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(445\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2671))\).

	Total	New	Old
Modular forms	223	223	0
Cusp forms	222	222	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.

\(2671\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(100\)	\(100\)	\(0\)		\(100\)	\(100\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(123\)	\(123\)	\(0\)		\(122\)	\(122\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

222 * q - q^2 - 2 * q^3 + 217 * q^4 - 6 * q^6 - 8 * q^7 - 9 * q^8 + 222 * q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^14 - 24 * q^15 + 203 * q^16 + 4 * q^17 + 3 * q^18 - 8 * q^19 - 12 * q^20 + 2 * q^21 - 2 * q^22 - 10 * q^23 - 6 * q^24 + 218 * q^25 - 14 * q^26 - 20 * q^27 - 34 * q^28 + 2 * q^29 - 38 * q^30 - 26 * q^31 - 29 * q^32 + 10 * q^33 - 14 * q^34 - 22 * q^35 + 185 * q^36 + 2 * q^37 + 12 * q^38 - 32 * q^39 - 8 * q^40 + 14 * q^41 + 8 * q^42 + 8 * q^43 - 22 * q^44 - 20 * q^45 - 6 * q^46 - 10 * q^47 + 8 * q^48 + 210 * q^49 - 5 * q^50 + 8 * q^51 - 10 * q^52 - 4 * q^53 + 2 * q^54 - 40 * q^55 - 6 * q^57 - 38 * q^58 - 10 * q^59 - 50 * q^60 + 10 * q^61 + 2 * q^62 - 50 * q^63 + 143 * q^64 - 10 * q^65 + 8 * q^66 - 24 * q^67 + 54 * q^68 - 16 * q^69 - 12 * q^70 - 30 * q^71 + 13 * q^72 + 12 * q^73 + 18 * q^74 + 22 * q^75 - 102 * q^76 - 14 * q^77 + 46 * q^78 - 40 * q^79 + 20 * q^80 + 230 * q^81 + 32 * q^82 + 8 * q^83 + 62 * q^84 + 10 * q^85 + 18 * q^86 + 22 * q^87 - 20 * q^88 + 36 * q^89 + 38 * q^90 - 10 * q^91 - 14 * q^92 + 20 * q^93 + 18 * q^94 - 12 * q^95 - 28 * q^96 - 2 * q^97 - 5 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2671))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2671
2671.2.a.a	$2671$	$2$	2671.a	1.a	$1$	$100$	$100$	$21.328$		None	✓	✓	✓	✓	2671.2.a.a	$1$	$1$	\(-15\)	\(-12\)	\(-33\)	\(-14\)		$+$	$+$		$\mathrm{SU}(2)$
2671.2.a.b	$2671$	$2$	2671.a	1.a	$1$	$122$	$122$	$21.328$		None	✓	✓	✓	✓	2671.2.a.b	$1$	$0$	\(14\)	\(10\)	\(33\)	\(6\)		$-$	$-$		$\mathrm{SU}(2)$