Space of modular forms of level 4001, weight 2, and trivial character

• Label: 4001.2.a
• Level: $4001$
• Weight: $2$
• Character orbit: 4001.a
• Rep. character: $\chi_{4001}(1,\cdot)$
• Character field: $\Q$
• Dimension: $333$
• Newform subspaces: $2$
• Sturm bound: $667$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(667\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4001))\).

	Total	New	Old
Modular forms	334	334	0
Cusp forms	333	333	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.

\(4001\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(149\)	\(149\)	\(0\)		\(149\)	\(149\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(185\)	\(185\)	\(0\)		\(184\)	\(184\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

333 * q - 3 * q^2 + 333 * q^4 - 4 * q^5 + 2 * q^7 - 9 * q^8 + 325 * q^9 - 2 * q^10 - 6 * q^11 - 2 * q^13 - 16 * q^14 - 6 * q^15 + 337 * q^16 - 10 * q^17 - 25 * q^18 - 26 * q^20 - 8 * q^21 - 2 * q^22 - 8 * q^23 - 18 * q^24 + 333 * q^25 - 6 * q^26 - 6 * q^27 - 2 * q^28 - 24 * q^29 - 32 * q^30 + 20 * q^31 - 21 * q^32 - 16 * q^33 - 2 * q^34 - 20 * q^35 + 323 * q^36 - 6 * q^39 - 16 * q^40 - 16 * q^41 + 10 * q^42 + 10 * q^43 - 22 * q^44 - 14 * q^45 + 6 * q^46 + 28 * q^48 + 327 * q^49 + 17 * q^50 - 38 * q^51 + 10 * q^52 - 2 * q^53 + 10 * q^54 + 8 * q^55 - 20 * q^56 - 6 * q^58 + 2 * q^59 - 12 * q^60 - 8 * q^61 + 4 * q^62 - 32 * q^63 + 323 * q^64 - 46 * q^65 + 24 * q^66 - 20 * q^67 + 22 * q^69 - 60 * q^70 - 6 * q^71 - 15 * q^72 - 2 * q^73 - 18 * q^74 + 4 * q^75 - 44 * q^76 + 6 * q^77 + 48 * q^78 + 14 * q^79 - 8 * q^80 + 285 * q^81 - 34 * q^82 - 2 * q^83 - 30 * q^85 + 28 * q^86 - 16 * q^87 - 28 * q^88 - 22 * q^89 + 54 * q^90 + 16 * q^91 + 22 * q^92 + 60 * q^93 + 10 * q^94 - 46 * q^95 - 8 * q^96 - 2 * q^97 - 29 * q^98 - 78 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		4001
4001.2.a.a	$4001$	$2$	4001.a	1.a	$1$	$149$	$149$	$31.948$		None	✓	✓	✓	✓	4001.2.a.a	$1$	$1$	\(-6\)	\(-28\)	\(-19\)	\(-47\)		$+$	$+$		$\mathrm{SU}(2)$
4001.2.a.b	$4001$	$2$	4001.a	1.a	$1$	$184$	$184$	$31.948$		None	✓	✓	✓	✓	4001.2.a.b	$1$	$0$	\(3\)	\(28\)	\(15\)	\(49\)		$-$	$-$		$\mathrm{SU}(2)$