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

• Label: 1014.2.g
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.g
• Rep. character: $\chi_{1014}(239,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $5$
• Sturm bound: $364$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(364\)
Trace bound:			\(7\)
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	100	320
Cusp forms	308	100	208
Eisenstein series	112	0	112

Trace form

100 * q + 12 * q^7 - 100 * q^16 + 12 * q^19 + 48 * q^27 - 12 * q^28 - 12 * q^31 - 36 * q^33 - 12 * q^37 - 48 * q^42 - 36 * q^45 + 36 * q^54 - 16 * q^55 + 36 * q^57 - 16 * q^61 + 36 * q^63 + 16 * q^66 + 12 * q^67 + 12 * q^73 + 12 * q^76 - 64 * q^79 + 16 * q^81 + 72 * q^85 + 32 * q^87 - 36 * q^93 + 80 * q^94 + 60 * q^97 - 36 * 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.g.a	$1014$	$2$	1014.g	39.f	$4$	$8$	$4$	$8.097$	8.0.959512576.1	None		✓			1014.2.g.a	$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}+(1+\beta _{2})q^{3}+\beta _{4}q^{4}+\beta _{5}q^{5}+\cdots\)
1014.2.g.b	$1014$	$2$	1014.g	39.f	$4$	$12$	$6$	$8.097$	12.0.\(\cdots\).52	None					78.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+\beta _{7}q^{3}-\beta _{8}q^{4}+(\beta _{5}-\beta _{9}+\cdots)q^{5}+\cdots\)
1014.2.g.c	$1014$	$2$	1014.g	39.f	$4$	$16$	$8$	$8.097$	16.0.\(\cdots\).9	None					78.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{11}q^{2}-\beta _{15}q^{3}+\beta _{12}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
1014.2.g.d	$1014$	$2$	1014.g	39.f	$4$	$16$	$8$	$8.097$	16.0.\(\cdots\).9	None					78.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{11}q^{2}+(-\beta _{2}-\beta _{5}-\beta _{6}+\beta _{15})q^{3}+\cdots\)
1014.2.g.e	$1014$	$2$	1014.g	39.f	$4$	$48$	$24$	$8.097$		None		✓	✓		1014.2.g.e	$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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