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

• Label: 264.2.b
• Level: $264$
• Weight: $2$
• Character orbit: 264.b
• Rep. character: $\chi_{264}(65,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	56	12	44
Cusp forms	40	12	28
Eisenstein series	16	0	16

Trace form

12 * q + 2 * q^3 + 6 * q^9 - 6 * q^15 + 8 * q^25 - 4 * q^27 + 12 * q^31 - 10 * q^33 - 12 * q^37 - 2 * q^45 - 4 * q^49 - 4 * q^55 - 44 * q^67 - 34 * q^69 - 40 * q^75 + 22 * q^81 - 24 * q^91 + 2 * q^93 - 52 * q^97 + 38 * 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.b.a	$264$	$2$	264.b	33.d	$2$	$6$	$6$	$2.108$	6.0.7388168.1	None		✓			264.2.b.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
264.2.b.b	$264$	$2$	264.b	33.d	$2$	$6$	$6$	$2.108$	6.0.7388168.1	None		✓			264.2.b.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(264, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(264, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)