Space of modular forms of level 266, weight 2, and Character 266.k

• Label: 266.2.k
• Level: $266$
• Weight: $2$
• Character orbit: 266.k
• Rep. character: $\chi_{266}(145,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	266.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(266, [\chi])\).

	Total	New	Old
Modular forms	88	24	64
Cusp forms	72	24	48
Eisenstein series	16	0	16

Trace form

24 * q - 24 * q^4 - 2 * q^7 - 8 * q^9 - 6 * q^13 + 30 * q^15 + 24 * q^16 + 24 * q^17 - 12 * q^19 + 18 * q^22 + 10 * q^23 - 12 * q^25 - 12 * q^26 + 2 * q^28 - 18 * q^29 - 8 * q^30 - 6 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^36 - 30 * q^37 - 18 * q^38 - 6 * q^39 + 6 * q^41 + 42 * q^42 + 8 * q^43 - 90 * q^45 + 6 * q^46 + 12 * q^47 + 6 * q^49 + 6 * q^52 - 6 * q^55 + 10 * q^57 + 4 * q^58 - 42 * q^59 - 30 * q^60 - 12 * q^61 + 26 * q^63 - 24 * q^64 + 24 * q^65 - 24 * q^68 + 24 * q^69 + 66 * q^71 + 78 * q^73 + 12 * q^74 + 66 * q^75 + 12 * q^76 - 26 * q^77 - 36 * q^78 - 12 * q^81 - 4 * q^85 + 12 * q^86 - 48 * q^87 - 18 * q^88 - 6 * q^91 - 10 * q^92 - 8 * q^93 - 30 * q^94 - 42 * q^95 - 30 * q^97 + 24 * q^98 - 42 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(266, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
266.2.k.a	$266$	$2$	266.k	133.i	$6$	$4$	$2$	$2.124$	\(\Q(\zeta_{12})\)	None		✓			266.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{3}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}-q^{4}+\cdots\)
266.2.k.b	$266$	$2$	266.k	133.i	$6$	$20$	$10$	$2.124$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		266.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+\beta _{9}q^{3}-q^{4}+(-\beta _{2}+\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(266, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(266, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)