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

• Label: 264.2.m
• Level: $264$
• Weight: $2$
• Character orbit: 264.m
• Rep. character: $\chi_{264}(197,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

44 * q - 4 * q^4 - 4 * q^9 + 4 * q^12 - 16 * q^15 + 4 * q^16 + 12 * q^22 + 20 * q^25 - 8 * q^31 - 12 * q^33 - 24 * q^34 - 36 * q^36 - 24 * q^42 - 28 * q^48 - 28 * q^49 - 8 * q^55 + 48 * q^58 - 24 * q^60 - 28 * q^64 + 28 * q^66 + 48 * q^70 - 40 * q^78 - 12 * q^81 - 8 * q^82 + 60 * q^88 + 8 * q^97

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.m.a	$264$	$2$	264.m	264.m	$2$	$4$	$4$	$2.108$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-6}) \)		✓			264.2.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+2\beta _{2}q^{5}+\cdots\)
264.2.m.b	$264$	$2$	264.m	264.m	$2$	$40$	$40$	$2.108$		None		✓	✓		264.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$