Space of modular forms of level 264, weight 2, and Character 264.w

• Label: 264.2.w
• Level: $264$
• Weight: $2$
• Character orbit: 264.w
• Rep. character: $\chi_{264}(59,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $176$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.w (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(264, [\chi])\).

	Total	New	Old
Modular forms	208	208	0
Cusp forms	176	176	0
Eisenstein series	32	32	0

Trace form

176 * q - 6 * q^3 - 6 * q^4 - 7 * q^6 - 6 * q^9 - 16 * q^10 - 2 * q^12 - 10 * q^16 - 7 * q^18 - 12 * q^19 - 32 * q^22 + 7 * q^24 - 40 * q^25 - 6 * q^27 + 14 * q^28 - 14 * q^30 - 18 * q^33 - 12 * q^34 - 29 * q^36 + 22 * q^40 - 50 * q^42 - 18 * q^46 - 40 * q^48 + 8 * q^49 - 18 * q^51 - 6 * q^52 - 82 * q^54 - 2 * q^57 - 18 * q^58 - 20 * q^60 + 30 * q^64 - 68 * q^66 - 96 * q^67 + 30 * q^72 - 12 * q^73 + 26 * q^75 + 60 * q^76 - 36 * q^78 + 2 * q^81 - 20 * q^82 + 86 * q^84 + 102 * q^88 - 18 * q^90 - 140 * q^91 + 58 * q^94 + 44 * q^96 + 4 * q^97 + 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(264, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
264.2.w.a	$264$	$2$	264.w	264.w	$10$	$8$	$2$	$2.108$	8.0.64000000.1	\(\Q(\sqrt{-2}) \)		✓			264.2.w.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{3}+2\beta _{2}q^{4}+(-2+\cdots)q^{6}+\cdots\)
264.2.w.b	$264$	$2$	264.w	264.w	$10$	$8$	$2$	$2.108$	8.0.64000000.1	\(\Q(\sqrt{-2}) \)		✓			264.2.w.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7})q^{3}+\cdots\)
264.2.w.c	$264$	$2$	264.w	264.w	$10$	$16$	$4$	$2.108$	16.0.\(\cdots\).9	None		✓			264.2.w.c	$8$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{11}q^{2}+(-1-\beta _{2}-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{3}+\cdots\)
264.2.w.d	$264$	$2$	264.w	264.w	$10$	$144$	$36$	$2.108$		None		✓	✓		264.2.w.d	$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$