Space of modular forms of level 3013, weight 2, and trivial character

• Label: 3013.2.a
• Level: $3013$
• Weight: $2$
• Character orbit: 3013.a
• Rep. character: $\chi_{3013}(1,\cdot)$
• Character field: $\Q$
• Dimension: $237$
• Newform subspaces: $4$
• Sturm bound: $528$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3013 = 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3013.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(528\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3013))\).

	Total	New	Old
Modular forms	266	237	29
Cusp forms	263	237	26
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.

\(23\)	\(131\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(61\)	\(60\)	\(1\)		\(61\)	\(60\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(69\)	\(58\)	\(11\)		\(68\)	\(58\)	\(10\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(72\)	\(68\)	\(4\)		\(71\)	\(68\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(64\)	\(51\)	\(13\)		\(63\)	\(51\)	\(12\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(125\)	\(111\)	\(14\)		\(124\)	\(111\)	\(13\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(141\)	\(126\)	\(15\)		\(139\)	\(126\)	\(13\)		\(2\)	\(0\)	\(2\)

Trace form

237 * q + q^2 + 237 * q^4 - 2 * q^5 + 12 * q^6 - 4 * q^7 + 9 * q^8 + 233 * q^9 - 10 * q^10 + 4 * q^11 - 26 * q^13 + 4 * q^15 + 217 * q^16 - 18 * q^17 + 29 * q^18 + 6 * q^20 - 12 * q^21 + 12 * q^22 + q^23 + 60 * q^24 + 231 * q^25 + 14 * q^26 + 12 * q^27 + 16 * q^28 - 2 * q^29 + 56 * q^30 - 8 * q^31 + 49 * q^32 + 30 * q^33 + 18 * q^34 + 10 * q^35 + 261 * q^36 - 30 * q^37 + 24 * q^38 - 34 * q^39 - 22 * q^40 + 2 * q^41 + 20 * q^42 - 28 * q^43 - 36 * q^44 - 36 * q^45 - q^46 + 20 * q^47 + 20 * q^48 + 225 * q^49 - 5 * q^50 + 4 * q^51 - 30 * q^52 - 16 * q^53 + 20 * q^54 + 4 * q^55 - 8 * q^56 - 24 * q^57 - 18 * q^58 - 16 * q^59 - 76 * q^60 - 50 * q^61 - 48 * q^62 - 30 * q^63 + 209 * q^64 - 20 * q^65 - 52 * q^66 + 28 * q^67 - 54 * q^68 + 4 * q^69 + 36 * q^70 - 44 * q^71 + 61 * q^72 - 34 * q^73 - 22 * q^74 - 14 * q^75 + 28 * q^76 + 4 * q^77 - 60 * q^78 - 8 * q^79 - 98 * q^80 + 245 * q^81 + 26 * q^82 + 36 * q^83 - 104 * q^84 - 4 * q^85 + 84 * q^86 + 32 * q^87 - 72 * q^88 + 28 * q^89 - 42 * q^90 - 48 * q^91 + 7 * q^92 + 8 * q^93 + 20 * q^94 - 12 * q^95 + 156 * q^96 - 14 * q^97 - 103 * q^98 + 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3013))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		23	131
3013.2.a.a	$3013$	$2$	3013.a	1.a	$1$	$51$	$51$	$24.059$		None	✓	✓	✓	✓	3013.2.a.a	$1$	$1$	\(-14\)	\(-20\)	\(-7\)	\(-5\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
3013.2.a.b	$3013$	$2$	3013.a	1.a	$1$	$58$	$58$	$24.059$		None	✓	✓	✓	✓	3013.2.a.b	$1$	$0$	\(13\)	\(16\)	\(9\)	\(7\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
3013.2.a.c	$3013$	$2$	3013.a	1.a	$1$	$60$	$60$	$24.059$		None	✓	✓	✓	✓	3013.2.a.c	$1$	$1$	\(-12\)	\(-18\)	\(-13\)	\(-13\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
3013.2.a.d	$3013$	$2$	3013.a	1.a	$1$	$68$	$68$	$24.059$		None	✓	✓	✓	✓	3013.2.a.d	$1$	$0$	\(14\)	\(22\)	\(9\)	\(7\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3013)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 2}\)