Space of modular forms of level 264, weight 3, and Character 264.p

• Label: 264.3.p
• Level: $264$
• Weight: $3$
• Character orbit: 264.p
• Rep. character: $\chi_{264}(131,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $7$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	264.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(264, [\chi])\).

	Total	New	Old
Modular forms	100	100	0
Cusp forms	92	92	0
Eisenstein series	8	8	0

Trace form

92 * q - 4 * q^3 - 4 * q^4 - 4 * q^9 - 20 * q^12 - 28 * q^16 - 84 * q^22 + 372 * q^25 - 4 * q^27 + 8 * q^33 - 104 * q^34 + 68 * q^36 + 24 * q^42 - 60 * q^48 + 468 * q^49 - 96 * q^58 - 112 * q^60 + 68 * q^64 - 340 * q^66 - 264 * q^67 - 352 * q^70 - 140 * q^75 - 360 * q^78 + 108 * q^81 - 232 * q^82 + 268 * q^88 - 592 * q^91 + 24 * q^97 + 32 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(264, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
264.3.p.a	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	\(\Q(\sqrt{22}) \)	\(\Q(\sqrt{-66}) \)	✓	✓			264.3.p.a	$4$	$0$	\(-4\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-3q^{3}+4q^{4}+\beta q^{5}+6q^{6}+\cdots\)
264.3.p.b	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		✓			264.3.p.b	$4$	$0$	\(-4\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+(1+\beta )q^{3}+4q^{4}+(-2-2\beta )q^{6}+\cdots\)
264.3.p.c	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-66}) \)	✓	✓			264.3.p.c	$4$	$0$	\(-4\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots\)
264.3.p.d	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	\(\Q(\sqrt{22}) \)	\(\Q(\sqrt{-66}) \)	✓	✓			264.3.p.a	$4$	$0$	\(4\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots\)
264.3.p.e	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		✓			264.3.p.b	$4$	$0$	\(4\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(2+2\beta )q^{6}+\cdots\)
264.3.p.f	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-66}) \)	✓	✓			264.3.p.c	$4$	$0$	\(4\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+3q^{3}+4q^{4}+\beta q^{5}+6q^{6}+\cdots\)
264.3.p.g	$264$	$3$	264.p	264.p	$2$	$80$	$80$	$7.193$		None		✓	✓		264.3.p.g	$8$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$