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

• Label: 1014.2.b
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.b
• Rep. character: $\chi_{1014}(337,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $7$
• Sturm bound: $364$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(364\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	210	26	184
Cusp forms	154	26	128
Eisenstein series	56	0	56

Trace form

\( 26 q - 2 q^{3} - 26 q^{4} + 26 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1014.2.b.a	$1014$	$2$	1014.b	13.b	$2$	$2$	$2$	$8.097$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-2iq^{7}+\cdots\)
1014.2.b.b	$1014$	$2$	1014.b	13.b	$2$	$2$	$2$	$8.097$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
1014.2.b.c	$1014$	$2$	1014.b	13.b	$2$	$2$	$2$	$8.097$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+q^{3}-q^{4}+3iq^{5}-iq^{6}+\cdots\)
1014.2.b.d	$1014$	$2$	1014.b	13.b	$2$	$4$	$4$	$8.097$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}-q^{3}-q^{4}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{6}+\cdots\)
1014.2.b.e	$1014$	$2$	1014.b	13.b	$2$	$4$	$4$	$8.097$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+q^{3}-q^{4}+(2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1014.2.b.f	$1014$	$2$	1014.b	13.b	$2$	$6$	$6$	$8.097$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{3}-q^{4}+(-2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1014.2.b.g	$1014$	$2$	1014.b	13.b	$2$	$6$	$6$	$8.097$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}+(\beta _{1}+\beta _{3}-\beta _{5})q^{5}+\cdots\)

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

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