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

• Label: 1014.2.i
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.i
• Rep. character: $\chi_{1014}(361,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $364$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(364\)
Trace bound:			\(10\)
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	48	372
Cusp forms	308	48	260
Eisenstein series	112	0	112

Trace form

48 * q + 24 * q^4 - 24 * q^9 - 4 * q^10 + 24 * q^14 + 12 * q^15 - 24 * q^16 + 12 * q^17 - 4 * q^22 + 16 * q^23 - 72 * q^25 - 20 * q^29 - 4 * q^30 - 12 * q^33 - 24 * q^35 + 24 * q^36 + 12 * q^37 - 8 * q^38 - 8 * q^40 - 48 * q^41 + 4 * q^42 + 8 * q^43 + 36 * q^49 - 24 * q^50 - 32 * q^51 + 24 * q^53 - 8 * q^55 + 12 * q^56 + 12 * q^58 + 48 * q^59 + 20 * q^62 - 48 * q^64 - 24 * q^66 + 48 * q^67 - 12 * q^68 + 4 * q^69 - 24 * q^71 + 8 * q^74 - 8 * q^75 + 32 * q^77 + 72 * q^79 - 24 * q^81 + 8 * q^82 + 12 * q^84 - 36 * q^85 + 4 * q^88 + 24 * q^89 + 8 * q^90 + 32 * q^92 + 24 * q^93 - 8 * q^94 - 8 * q^95 - 24 * q^98

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.i.a	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.i.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.b	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.e.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.c	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.b.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.d	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.a.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.e	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.e.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.f	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	\(\Q(\zeta_{12})\)	None					78.2.i.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.g	$1014$	$2$	1014.i	13.e	$6$	$12$	$6$	$8.097$	12.0.\(\cdots\).1	None		✓			1014.2.a.m	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{2}-\beta _{7}q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1014.2.i.h	$1014$	$2$	1014.i	13.e	$6$	$12$	$6$	$8.097$	12.0.\(\cdots\).1	None		✓			1014.2.a.l	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+(1-\beta _{7})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)