Space of modular forms of level 264, weight 4, and Character 264.f

• Label: 264.4.f
• Level: $264$
• Weight: $4$
• Character orbit: 264.f
• Rep. character: $\chi_{264}(133,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	264.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(264, [\chi])\).

	Total	New	Old
Modular forms	148	60	88
Cusp forms	140	60	80
Eisenstein series	8	0	8

Trace form

60 * q - 12 * q^4 + 12 * q^6 + 84 * q^8 - 540 * q^9 - 48 * q^10 + 236 * q^14 + 120 * q^15 - 188 * q^16 - 104 * q^17 + 308 * q^20 - 228 * q^24 - 1588 * q^25 - 316 * q^26 + 584 * q^28 - 336 * q^30 + 1272 * q^31 - 140 * q^32 + 40 * q^34 + 108 * q^36 + 776 * q^38 + 576 * q^40 - 472 * q^41 + 660 * q^42 - 616 * q^44 - 640 * q^46 + 816 * q^47 - 528 * q^48 + 2220 * q^49 - 3192 * q^50 + 1488 * q^52 - 108 * q^54 - 880 * q^55 + 2628 * q^56 + 336 * q^57 - 320 * q^58 + 1692 * q^60 + 896 * q^62 - 3492 * q^64 + 3488 * q^65 - 1520 * q^68 + 2048 * q^70 + 224 * q^71 - 756 * q^72 - 1912 * q^73 - 2936 * q^74 + 3376 * q^76 - 36 * q^78 - 2832 * q^79 - 1212 * q^80 + 4860 * q^81 + 2160 * q^82 + 2256 * q^84 - 680 * q^86 + 396 * q^88 + 440 * q^89 + 432 * q^90 - 7604 * q^92 + 656 * q^94 - 7728 * q^95 - 4668 * q^96 + 3400 * q^97 + 1304 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(264, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
264.4.f.a	$264$	$4$	264.f	8.b	$2$	$2$	$2$	$15.577$	\(\Q(\sqrt{-1}) \)	None		✓			264.4.f.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-72\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2 i-2)q^{2}+3 i q^{3}-8 i q^{4}+12 i q^{5}+\cdots\)
264.4.f.b	$264$	$4$	264.f	8.b	$2$	$28$	$28$	$15.577$		None		✓			264.4.f.b	$2$	$0$	\(4\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{2}]$
264.4.f.c	$264$	$4$	264.f	8.b	$2$	$30$	$30$	$15.577$		None		✓	✓		264.4.f.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(84\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(264, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(264, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)