Space of modular forms of level 1014, weight 2, and Character 1014.e

• Label: 1014.2.e
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.e
• Rep. character: $\chi_{1014}(529,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $52$
• Newform subspaces: $14$
• Sturm bound: $364$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(364\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

	Total	New	Old
Modular forms	420	52	368
Cusp forms	308	52	256
Eisenstein series	112	0	112

Trace form

52 * q - 2 * q^2 - 26 * q^4 - 4 * q^5 + 4 * q^8 - 26 * q^9 - 2 * q^10 + 8 * q^11 + 8 * q^14 + 4 * q^15 - 26 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^20 - 8 * q^21 - 12 * q^22 - 8 * q^23 + 72 * q^25 - 18 * q^29 - 4 * q^30 + 16 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 - 26 * q^36 - 18 * q^37 + 8 * q^38 + 4 * q^40 + 2 * q^41 - 4 * q^42 - 8 * q^43 - 16 * q^44 + 2 * q^45 - 16 * q^47 - 46 * q^49 + 32 * q^51 + 20 * q^53 + 8 * q^55 - 4 * q^56 - 8 * q^57 + 6 * q^58 - 8 * q^59 - 8 * q^60 - 30 * q^61 + 4 * q^62 + 52 * q^64 + 8 * q^66 - 8 * q^67 - 2 * q^68 - 20 * q^69 + 16 * q^70 - 8 * q^71 - 2 * q^72 + 52 * q^73 + 18 * q^74 + 8 * q^75 + 56 * q^79 + 2 * q^80 - 26 * q^81 - 6 * q^82 + 4 * q^84 - 14 * q^85 + 8 * q^87 - 12 * q^88 + 20 * q^89 + 4 * q^90 + 16 * q^92 - 16 * q^94 - 8 * q^95 + 12 * q^97 + 6 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1014.2.e.a	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	\(\Q(\sqrt{-3}) \)	None					78.2.e.a	$2$	$0$	\(-1\)	\(-1\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.b	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	\(\Q(\sqrt{-3}) \)	None					78.2.b.a	$2$	$0$	\(-1\)	\(-1\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.c	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	\(\Q(\sqrt{-3}) \)	None					78.2.a.a	$2$	$0$	\(-1\)	\(1\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.d	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	\(\Q(\sqrt{-3}) \)	None					78.2.e.b	$2$	$0$	\(-1\)	\(1\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.e	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	\(\Q(\sqrt{-3}) \)	None					78.2.b.a	$2$	$0$	\(1\)	\(-1\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.f	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	\(\Q(\sqrt{-3}) \)	None					78.2.a.a	$2$	$0$	\(1\)	\(1\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.g	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.i.a	$2$	$0$	\(-2\)	\(-2\)	\(8\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{2}+(\beta_1-1)q^{3}-\beta_1 q^{4}+\cdots\)
1014.2.e.h	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.i.b	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(6\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_1 q^{2}+\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots\)
1014.2.e.i	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.i.a	$2$	$0$	\(2\)	\(-2\)	\(-8\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta_1 q^{2}-\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots\)
1014.2.e.j	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.i.b	$2$	$0$	\(2\)	\(2\)	\(0\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta_1 q^{2}+\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots\)
1014.2.e.k	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.m	$2$	$0$	\(-3\)	\(-3\)	\(-6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{5})q^{2}+(-1+\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots\)
1014.2.e.l	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.l	$2$	$0$	\(-3\)	\(3\)	\(2\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{5})q^{2}+(1-\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots\)
1014.2.e.m	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.m	$2$	$0$	\(3\)	\(-3\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}-\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.2.e.n	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.l	$2$	$0$	\(3\)	\(3\)	\(-2\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

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