Space of modular forms of level 1014, weight 2, and trivial character

• Label: 1014.2.a
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.a
• Rep. character: $\chi_{1014}(1,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $15$
• Sturm bound: $364$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(364\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1014))\).

	Total	New	Old
Modular forms	210	27	183
Cusp forms	155	27	128
Eisenstein series	55	0	55

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(5\)
\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(6\)
Plus space			\(+\)	\(7\)
Minus space			\(-\)	\(20\)

Trace form

27 * q + q^2 + q^3 + 27 * q^4 - 2 * q^5 - q^6 - 4 * q^7 + q^8 + 27 * q^9 + 2 * q^10 + 4 * q^11 + q^12 + 8 * q^14 + 2 * q^15 + 27 * q^16 + 2 * q^17 + q^18 + 8 * q^19 - 2 * q^20 + 4 * q^21 + 8 * q^23 - q^24 + 37 * q^25 + q^27 - 4 * q^28 + 6 * q^29 - 2 * q^30 + 4 * q^31 + q^32 - 4 * q^33 + 2 * q^34 + 27 * q^36 + 2 * q^37 - 4 * q^38 + 2 * q^40 + 10 * q^41 - 4 * q^42 + 4 * q^43 + 4 * q^44 - 2 * q^45 - 8 * q^47 + q^48 + 31 * q^49 - q^50 + 10 * q^51 + 22 * q^53 - q^54 + 16 * q^55 + 8 * q^56 - 8 * q^57 + 6 * q^58 - 4 * q^59 + 2 * q^60 + 14 * q^61 - 4 * q^63 + 27 * q^64 + 4 * q^66 + 16 * q^67 + 2 * q^68 + 8 * q^69 + 8 * q^70 + 8 * q^71 + q^72 - 2 * q^73 - 2 * q^74 - q^75 + 8 * q^76 + 24 * q^77 + 12 * q^79 - 2 * q^80 + 27 * q^81 - 6 * q^82 - 12 * q^83 + 4 * q^84 - 4 * q^85 + 4 * q^86 + 10 * q^87 - 14 * q^89 + 2 * q^90 + 8 * q^92 - 4 * q^93 + 16 * q^94 + 32 * q^95 - q^96 - 10 * q^97 + 9 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	13
1014.2.a.a	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓		✓	✓	78.2.e.b	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
1014.2.a.b	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓				78.2.b.a	$1$	$1$	\(-1\)	\(1\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1014.2.a.c	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓				78.2.e.a	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
1014.2.a.d	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓				78.2.a.a	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-4q^{7}+\cdots\)
1014.2.a.e	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓				78.2.e.b	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
1014.2.a.f	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓		✓	✓	78.2.e.a	$1$	$1$	\(1\)	\(1\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-2q^{7}+\cdots\)
1014.2.a.g	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	\(\Q\)	None	✓				78.2.b.a	$1$	$0$	\(1\)	\(1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
1014.2.a.h	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	\(\Q(\sqrt{3}) \)	None	✓				78.2.i.b	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+(3-\beta )q^{7}+\cdots\)
1014.2.a.i	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	\(\Q(\sqrt{3}) \)	None	✓		✓		78.2.i.a	$1$	$1$	\(-2\)	\(2\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
1014.2.a.j	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	\(\Q(\sqrt{3}) \)	None	✓		✓	✓	78.2.i.b	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
1014.2.a.k	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	\(\Q(\sqrt{3}) \)	None	✓				78.2.i.a	$1$	$0$	\(2\)	\(2\)	\(4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
1014.2.a.l	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		1014.2.a.l	$1$	$0$	\(-3\)	\(-3\)	\(-1\)	\(-9\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(1-3\beta _{1}+\beta _{2})q^{5}+\cdots\)
1014.2.a.m	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		1014.2.a.m	$1$	$0$	\(-3\)	\(3\)	\(3\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1014.2.a.n	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		1014.2.a.l	$1$	$0$	\(3\)	\(-3\)	\(1\)	\(9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
1014.2.a.o	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		1014.2.a.m	$1$	$0$	\(3\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1014)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)