Space of modular forms of level 8013, weight 2, and trivial character

• Label: 8013.2.a
• Level: $8013$
• Weight: $2$
• Character orbit: 8013.a
• Rep. character: $\chi_{8013}(1,\cdot)$
• Character field: $\Q$
• Dimension: $445$
• Newform subspaces: $4$
• Sturm bound: $1781$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1781\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8013))\).

	Total	New	Old
Modular forms	892	445	447
Cusp forms	889	445	444
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.

\(3\)	\(2671\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(216\)	\(116\)	\(100\)		\(216\)	\(116\)	\(100\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(229\)	\(106\)	\(123\)		\(228\)	\(106\)	\(122\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(230\)	\(129\)	\(101\)		\(229\)	\(129\)	\(100\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(217\)	\(94\)	\(123\)		\(216\)	\(94\)	\(122\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(433\)	\(210\)	\(223\)		\(432\)	\(210\)	\(222\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(459\)	\(235\)	\(224\)		\(457\)	\(235\)	\(222\)		\(2\)	\(0\)	\(2\)

Trace form

445 * q + q^2 + q^3 + 449 * q^4 - 2 * q^5 + 3 * q^6 + 8 * q^7 + 9 * q^8 + 445 * q^9 + 2 * q^10 - q^12 + 2 * q^13 + 16 * q^14 + 6 * q^15 + 461 * q^16 - 6 * q^17 + q^18 + 8 * q^19 + 22 * q^20 + 4 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 439 * q^25 + 2 * q^26 + q^27 + 24 * q^28 + 2 * q^29 + 2 * q^30 + 24 * q^31 + 29 * q^32 + 4 * q^33 + 14 * q^34 + 16 * q^35 + 449 * q^36 + 2 * q^37 - 12 * q^38 + 6 * q^39 - 6 * q^40 - 22 * q^41 - 20 * q^42 - 20 * q^43 + 16 * q^44 - 2 * q^45 + 24 * q^47 + 15 * q^48 + 453 * q^49 - 17 * q^50 - 2 * q^51 - 14 * q^52 + 6 * q^53 + 3 * q^54 + 40 * q^55 + 40 * q^56 + 18 * q^58 + 8 * q^59 + 22 * q^60 - 6 * q^61 + 4 * q^62 + 8 * q^63 + 505 * q^64 - 44 * q^65 + 12 * q^66 + 24 * q^67 - 58 * q^68 - 36 * q^70 + 32 * q^71 + 9 * q^72 - 18 * q^73 + 10 * q^74 - 17 * q^75 + 100 * q^76 + 60 * q^77 + 2 * q^78 + 24 * q^79 - 6 * q^80 + 445 * q^81 - 54 * q^82 + 20 * q^83 + 20 * q^84 - 8 * q^85 + 44 * q^86 + 6 * q^87 + 40 * q^88 - 30 * q^89 + 2 * q^90 - 4 * q^91 + 4 * q^92 - 12 * q^93 + 8 * q^95 + 19 * q^96 + 14 * q^97 + 41 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8013))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	2671
8013.2.a.a	$8013$	$2$	8013.a	1.a	$1$	$94$	$94$	$63.984$		None	✓	✓	✓	✓	8013.2.a.a	$1$	$1$	\(-13\)	\(94\)	\(-14\)	\(-55\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8013.2.a.b	$8013$	$2$	8013.a	1.a	$1$	$106$	$106$	$63.984$		None	✓	✓	✓	✓	8013.2.a.b	$1$	$0$	\(15\)	\(-106\)	\(16\)	\(35\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8013.2.a.c	$8013$	$2$	8013.a	1.a	$1$	$116$	$116$	$63.984$		None	✓	✓	✓	✓	8013.2.a.c	$1$	$1$	\(-16\)	\(-116\)	\(-20\)	\(-33\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8013.2.a.d	$8013$	$2$	8013.a	1.a	$1$	$129$	$129$	$63.984$		None	✓	✓	✓	✓	8013.2.a.d	$1$	$0$	\(15\)	\(129\)	\(16\)	\(61\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8013)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2671))\)\(^{\oplus 2}\)