Space of modular forms of level 1666, weight 2, and Character 1666.b

• Label: 1666.2.b
• Level: $1666$
• Weight: $2$
• Character orbit: 1666.b
• Rep. character: $\chi_{1666}(883,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $15$
• Sturm bound: $504$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(504\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1666, [\chi])\).

	Total	New	Old
Modular forms	268	62	206
Cusp forms	236	62	174
Eisenstein series	32	0	32

Trace form

\( 62 q - 2 q^{2} + 62 q^{4} - 2 q^{8} - 54 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1666, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1666.2.b.a	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+3iq^{3}+q^{4}-3iq^{6}-q^{8}+\cdots\)
1666.2.b.b	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+3iq^{3}+q^{4}-3iq^{6}-q^{8}+\cdots\)
1666.2.b.c	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
1666.2.b.d	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-q^{8}+3q^{9}-2q^{13}+q^{16}+\cdots\)
1666.2.b.e	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
1666.2.b.f	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
1666.2.b.g	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	\(\Q(\sqrt{-2}, \sqrt{15})\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
1666.2.b.h	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	\(\Q(\sqrt{-2}, \sqrt{15})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\)
1666.2.b.i	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+q^{4}+(\zeta_{8}+\cdots)q^{6}+\cdots\)
1666.2.b.j	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	\(\Q(\sqrt{-2}, \sqrt{15})\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
1666.2.b.k	$1666$	$2$	1666.b	17.b	$2$	$6$	$6$	$13.303$	6.0.84345856.2	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
1666.2.b.l	$1666$	$2$	1666.b	17.b	$2$	$6$	$6$	$13.303$	6.0.84345856.2	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
1666.2.b.m	$1666$	$2$	1666.b	17.b	$2$	$6$	$6$	$13.303$	6.0.350464.1	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
1666.2.b.n	$1666$	$2$	1666.b	17.b	$2$	$8$	$8$	$13.303$	8.0.\(\cdots\).5	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
1666.2.b.o	$1666$	$2$	1666.b	17.b	$2$	$8$	$8$	$13.303$	8.0.\(\cdots\).3	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)